diff --git a/CMAKE/LAPACKTestHelpers.cmake b/CMAKE/LAPACKTestHelpers.cmake
index 609f32045..d0f683ab2 100644
--- a/CMAKE/LAPACKTestHelpers.cmake
+++ b/CMAKE/LAPACKTestHelpers.cmake
@@ -44,9 +44,9 @@ function(lapack_no_constant_propagation_flag out_var)
   endif()
 endfunction()
 
-# Disable it for the ?errcxx drivers among ARGN, which manufacture their NaN
-# with SQRT( -ONE ).  Call this with every source list such a driver is built
-# from: the generated _64 and _TEST copies need it as much as the originals.
+# Disable it for the CXX and LS error-exit tests among ARGN, which
+# manufacture NaNs. Call this with every source list: the generated _64
+# and _TEST copies need it as much as the originals.
 function(lapack_nag_disable_constant_propagation)
   lapack_no_constant_propagation_flag(flag)
   if(NOT flag)
@@ -54,7 +54,7 @@ function(lapack_nag_disable_constant_propagation)
   endif()
   foreach(source IN LISTS ARGN)
     get_filename_component(name "${source}" NAME)
-    if(name MATCHES "^[scdz]errcxx(_[A-Za-z0-9]+)*\\.f$")
+    if(name MATCHES "^[scdz]err(cxx|ls)(_[A-Za-z0-9]+)*\\.f$")
       set_source_files_properties("${source}"
         PROPERTIES COMPILE_OPTIONS "${flag}")
     endif()
diff --git a/SRC/cgelsd.f b/SRC/cgelsd.f
index 11ab07ac2..5aa611b46 100644
--- a/SRC/cgelsd.f
+++ b/SRC/cgelsd.f
@@ -192,6 +192,8 @@
 *>          > 0:  the algorithm for computing the SVD failed to converge;
 *>                if INFO = i, i off-diagonal elements of an intermediate
 *>                bidiagonal form did not converge to zero.
+*>                INFO = 1 is also returned if A contains a NaN or an
+*>                infinity.
 *> \endverbatim
 *
 *  Authors:
diff --git a/SRC/clalsd.f b/SRC/clalsd.f
index 3a16ddd13..737eaed8f 100644
--- a/SRC/clalsd.f
+++ b/SRC/clalsd.f
@@ -153,6 +153,7 @@
 *>         > 0:  The algorithm failed to compute a singular value while
 *>               working on the submatrix lying in rows and columns
 *>               INFO/(N+1) through MOD(INFO,N+1).
+*>         = 1:  also if D or E contains a NaN.
 *> \endverbatim
 *
 *  Authors:
@@ -212,8 +213,8 @@ SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
 *     .. External Functions ..
       INTEGER            ISAMAX
       REAL               SLAMCH, SLANST
-      LOGICAL            LSAME
-      EXTERNAL           ISAMAX, SLAMCH, SLANST, LSAME
+      LOGICAL            SISNAN, LSAME
+      EXTERNAL           ISAMAX, SLAMCH, SLANST, SISNAN, LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CCOPY, CLACPY, CLALSA, CLASCL, CLASET,
@@ -261,6 +262,8 @@ SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       ELSE IF( N.EQ.1 ) THEN
          IF( D( 1 ).EQ.ZERO ) THEN
             CALL CLASET( 'A', 1, NRHS, CZERO, CZERO, B, LDB )
+         ELSE IF( SISNAN( D( 1 ) ) ) THEN
+            INFO = 1
          ELSE
             RANK = 1
             CALL CLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB,
@@ -304,6 +307,9 @@ SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       IF( ORGNRM.EQ.ZERO ) THEN
          CALL CLASET( 'A', N, NRHS, CZERO, CZERO, B, LDB )
          RETURN
+      ELSE IF( SISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
       END IF
 *
       CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
diff --git a/SRC/dbdsdc.f b/SRC/dbdsdc.f
index 21907669f..8ec720f15 100644
--- a/SRC/dbdsdc.f
+++ b/SRC/dbdsdc.f
@@ -172,6 +172,8 @@
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>          > 0:  The algorithm failed to compute a singular value.
 *>                The update process of divide and conquer failed.
+*>          = 1:  also if D or E contains a NaN and the divide and
+*>                conquer path is taken (COMPQ = 'I' or 'P', N > SMLSIZ).
 *> \endverbatim
 *
 *  Authors:
@@ -227,10 +229,10 @@ SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q,
       DOUBLE PRECISION   CS, EPS, ORGNRM, P, R, SN
 *     ..
 *     .. External Functions ..
-      LOGICAL            LSAME
+      LOGICAL            DISNAN, LSAME
       INTEGER            ILAENV
       DOUBLE PRECISION   DLAMCH, DLANST
-      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANST
+      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANST, DISNAN
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DLARTG, DLASCL, DLASD0, DLASDA,
@@ -370,8 +372,12 @@ SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q,
 *     Scale.
 *
       ORGNRM = DLANST( 'M', N, D, E )
-      IF( ORGNRM.EQ.ZERO )
-     $   RETURN
+      IF( ORGNRM.EQ.ZERO ) THEN
+         RETURN
+      ELSE IF( DISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
+      END IF
       CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, IERR )
       CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, NM1, 1, E, NM1, IERR )
 *
diff --git a/SRC/dgelsd.f b/SRC/dgelsd.f
index 0043f2593..306e8d8b1 100644
--- a/SRC/dgelsd.f
+++ b/SRC/dgelsd.f
@@ -176,6 +176,8 @@
 *>          > 0:  the algorithm for computing the SVD failed to converge;
 *>                if INFO = i, i off-diagonal elements of an intermediate
 *>                bidiagonal form did not converge to zero.
+*>                INFO = 1 is also returned if A contains a NaN or an
+*>                infinity.
 *> \endverbatim
 *
 *  Authors:
diff --git a/SRC/dlalsd.f b/SRC/dlalsd.f
index f5dbfc601..3355713ec 100644
--- a/SRC/dlalsd.f
+++ b/SRC/dlalsd.f
@@ -146,6 +146,7 @@
 *>         > 0:  The algorithm failed to compute a singular value while
 *>               working on the submatrix lying in rows and columns
 *>               INFO/(N+1) through MOD(INFO,N+1).
+*>         = 1:  also if D or E contains a NaN.
 *> \endverbatim
 *
 *  Authors:
@@ -200,8 +201,8 @@ SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
 *     .. External Functions ..
       INTEGER            IDAMAX
       DOUBLE PRECISION   DLAMCH, DLANST
-      LOGICAL            LSAME
-      EXTERNAL           IDAMAX, DLAMCH, DLANST, LSAME
+      LOGICAL            DISNAN, LSAME
+      EXTERNAL           IDAMAX, DLAMCH, DLANST, DISNAN, LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DCOPY, DGEMM, DLACPY, DLALSA, DLARTG,
@@ -248,6 +249,8 @@ SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       ELSE IF( N.EQ.1 ) THEN
          IF( D( 1 ).EQ.ZERO ) THEN
             CALL DLASET( 'A', 1, NRHS, ZERO, ZERO, B, LDB )
+         ELSE IF( DISNAN( D( 1 ) ) ) THEN
+            INFO = 1
          ELSE
             RANK = 1
             CALL DLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB,
@@ -291,6 +294,9 @@ SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       IF( ORGNRM.EQ.ZERO ) THEN
          CALL DLASET( 'A', N, NRHS, ZERO, ZERO, B, LDB )
          RETURN
+      ELSE IF( DISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
       END IF
 *
       CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
diff --git a/SRC/sbdsdc.f b/SRC/sbdsdc.f
index ba285eab4..90135c6c1 100644
--- a/SRC/sbdsdc.f
+++ b/SRC/sbdsdc.f
@@ -172,6 +172,8 @@
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>          > 0:  The algorithm failed to compute a singular value.
 *>                The update process of divide and conquer failed.
+*>          = 1:  also if D or E contains a NaN and the divide and
+*>                conquer path is taken (COMPQ = 'I' or 'P', N > SMLSIZ).
 *> \endverbatim
 *
 *  Authors:
@@ -227,10 +229,10 @@ SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q,
       REAL               CS, EPS, ORGNRM, P, R, SN
 *     ..
 *     .. External Functions ..
-      LOGICAL            LSAME
+      LOGICAL            SISNAN, LSAME
       INTEGER            ILAENV
       REAL               SLAMCH, SLANST
-      EXTERNAL           SLAMCH, SLANST, ILAENV, LSAME
+      EXTERNAL           SLAMCH, SLANST, ILAENV, LSAME, SISNAN
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SLARTG, SLASCL, SLASD0, SLASDA,
@@ -370,8 +372,12 @@ SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q,
 *     Scale.
 *
       ORGNRM = SLANST( 'M', N, D, E )
-      IF( ORGNRM.EQ.ZERO )
-     $   RETURN
+      IF( ORGNRM.EQ.ZERO ) THEN
+         RETURN
+      ELSE IF( SISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
+      END IF
       CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, IERR )
       CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, NM1, 1, E, NM1, IERR )
 *
diff --git a/SRC/sgelsd.f b/SRC/sgelsd.f
index 423450e1c..ebcfbf334 100644
--- a/SRC/sgelsd.f
+++ b/SRC/sgelsd.f
@@ -177,6 +177,8 @@
 *>          > 0:  the algorithm for computing the SVD failed to converge;
 *>                if INFO = i, i off-diagonal elements of an intermediate
 *>                bidiagonal form did not converge to zero.
+*>                INFO = 1 is also returned if A contains a NaN or an
+*>                infinity.
 *> \endverbatim
 *
 *  Authors:
diff --git a/SRC/slalsd.f b/SRC/slalsd.f
index 722b724d2..d46924abf 100644
--- a/SRC/slalsd.f
+++ b/SRC/slalsd.f
@@ -146,6 +146,7 @@
 *>         > 0:  The algorithm failed to compute a singular value while
 *>               working on the submatrix lying in rows and columns
 *>               INFO/(N+1) through MOD(INFO,N+1).
+*>         = 1:  also if D or E contains a NaN.
 *> \endverbatim
 *
 *  Authors:
@@ -200,8 +201,8 @@ SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
 *     .. External Functions ..
       INTEGER            ISAMAX
       REAL               SLAMCH, SLANST
-      LOGICAL            LSAME
-      EXTERNAL           ISAMAX, SLAMCH, SLANST, LSAME
+      LOGICAL            SISNAN, LSAME
+      EXTERNAL           ISAMAX, SLAMCH, SLANST, SISNAN, LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SGEMM, SLACPY, SLALSA, SLARTG,
@@ -248,6 +249,8 @@ SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       ELSE IF( N.EQ.1 ) THEN
          IF( D( 1 ).EQ.ZERO ) THEN
             CALL SLASET( 'A', 1, NRHS, ZERO, ZERO, B, LDB )
+         ELSE IF( SISNAN( D( 1 ) ) ) THEN
+            INFO = 1
          ELSE
             RANK = 1
             CALL SLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB,
@@ -291,6 +294,9 @@ SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       IF( ORGNRM.EQ.ZERO ) THEN
          CALL SLASET( 'A', N, NRHS, ZERO, ZERO, B, LDB )
          RETURN
+      ELSE IF( SISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
       END IF
 *
       CALL SLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
diff --git a/SRC/zgelsd.f b/SRC/zgelsd.f
index c5adf6c9e..6426dc285 100644
--- a/SRC/zgelsd.f
+++ b/SRC/zgelsd.f
@@ -192,6 +192,8 @@
 *>          > 0:  the algorithm for computing the SVD failed to converge;
 *>                if INFO = i, i off-diagonal elements of an intermediate
 *>                bidiagonal form did not converge to zero.
+*>                INFO = 1 is also returned if A contains a NaN or an
+*>                infinity.
 *> \endverbatim
 *
 *  Authors:
diff --git a/SRC/zlalsd.f b/SRC/zlalsd.f
index db4ddec92..0d194db3c 100644
--- a/SRC/zlalsd.f
+++ b/SRC/zlalsd.f
@@ -154,6 +154,7 @@
 *>         > 0:  The algorithm failed to compute a singular value while
 *>               working on the submatrix lying in rows and columns
 *>               INFO/(N+1) through MOD(INFO,N+1).
+*>         = 1:  also if D or E contains a NaN.
 *> \endverbatim
 *
 *  Authors:
@@ -213,8 +214,8 @@ SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
 *     .. External Functions ..
       INTEGER            IDAMAX
       DOUBLE PRECISION   DLAMCH, DLANST
-      LOGICAL            LSAME
-      EXTERNAL           IDAMAX, DLAMCH, DLANST, LSAME
+      LOGICAL            DISNAN, LSAME
+      EXTERNAL           IDAMAX, DLAMCH, DLANST, DISNAN, LSAME
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DGEMM, DLARTG, DLASCL, DLASDA, DLASDQ,
@@ -262,6 +263,8 @@ SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       ELSE IF( N.EQ.1 ) THEN
          IF( D( 1 ).EQ.ZERO ) THEN
             CALL ZLASET( 'A', 1, NRHS, CZERO, CZERO, B, LDB )
+         ELSE IF( DISNAN( D( 1 ) ) ) THEN
+            INFO = 1
          ELSE
             RANK = 1
             CALL ZLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB,
@@ -305,6 +308,9 @@ SUBROUTINE ZLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND,
       IF( ORGNRM.EQ.ZERO ) THEN
          CALL ZLASET( 'A', N, NRHS, CZERO, CZERO, B, LDB )
          RETURN
+      ELSE IF( DISNAN( ORGNRM ) ) THEN
+         INFO = 1
+         RETURN
       END IF
 *
       CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
diff --git a/TESTING/LIN/CMakeLists.txt b/TESTING/LIN/CMakeLists.txt
index 2313fa0c4..af64f74f4 100644
--- a/TESTING/LIN/CMakeLists.txt
+++ b/TESTING/LIN/CMakeLists.txt
@@ -222,7 +222,8 @@ else()
 endif()
 
 lapack_nag_disable_constant_propagation(
-  serrcxx.f cerrcxx.f derrcxx.f zerrcxx.f)
+  serrcxx.f cerrcxx.f derrcxx.f zerrcxx.f
+  serrls.f cerrls.f derrls.f zerrls.f)
 
 set(DSLINTST dchkab.f
 	ddrvab.f ddrvac.f derrab.f derrac.f dget08.f
diff --git a/TESTING/LIN/cerrls.f b/TESTING/LIN/cerrls.f
index 5c0daad02..2e97c11ea 100644
--- a/TESTING/LIN/cerrls.f
+++ b/TESTING/LIN/cerrls.f
@@ -66,18 +66,18 @@ SUBROUTINE CERRLS( PATH, NUNIT )
 *  =====================================================================
 *
 *     .. Parameters ..
-      INTEGER            NMAX
-      PARAMETER          ( NMAX = 2 )
+      INTEGER            NMAX, LW, LIW
+      PARAMETER          ( NMAX = 2, LW = 1000, LIW = 30 )
 *     ..
 *     .. Local Scalars ..
       CHARACTER*2        C2
       INTEGER            INFO, IRNK
-      REAL               RCOND
+      REAL               NAN, ONE, RCOND
 *     ..
 *     .. Local Arrays ..
-      INTEGER            IP( NMAX )
-      REAL               RW( NMAX ), S( NMAX )
-      COMPLEX            A( NMAX, NMAX ), B( NMAX, NMAX ), W( NMAX )
+      INTEGER            IP( LIW )
+      REAL               RW( LW ), S( NMAX )
+      COMPLEX            A( NMAX, NMAX ), B( NMAX, NMAX ), W( LW )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -96,6 +96,9 @@ SUBROUTINE CERRLS( PATH, NUNIT )
       COMMON             / INFOC / INFOT, NOUT, OK, LERR
       COMMON             / SRNAMC / SRNAMT
 *     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          SQRT
+*     ..
 *     .. Executable Statements ..
 *
       NOUT = NUNIT
@@ -271,6 +274,26 @@ SUBROUTINE CERRLS( PATH, NUNIT )
          CALL CGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, 1,
      $                RW, IP, INFO )
          CALL CHKXER( 'CGELSD', INFOT, NOUT, LERR, OK )
+*
+*        CGELSD must return INFO = 1, without calling XERBLA, when A
+*        contains a NaN: the NaN norm would otherwise be rejected by
+*        SLASCL inside CLALSD.
+*
+         ONE = 1.0E+0
+         NAN = SQRT( -ONE )
+         A( 2, 2 ) = NAN
+         B( 1, 1 ) = ( 1.0E+0, 0.0E+0 )
+         B( 2, 1 ) = ( 1.0E+0, 0.0E+0 )
+         RCOND = -1.0E+0
+         SRNAMT = 'CGELSD'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL CGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, LW, RW,
+     $                IP, INFO )
+         IF( LERR .OR. INFO.NE.1 ) THEN
+            WRITE( NOUT, FMT = 9999 )INFO
+            OK = .FALSE.
+         END IF
       END IF
 *
 *     Print a summary line.
@@ -278,6 +301,9 @@ SUBROUTINE CERRLS( PATH, NUNIT )
       CALL ALAESM( PATH, OK, NOUT )
 *
       RETURN
+*
+ 9999 FORMAT( ' *** CGELSD on a matrix with a NaN returned INFO = ', I6,
+     $      ' instead of 1 ***' )
 *
 *     End of CERRLS
 *
diff --git a/TESTING/LIN/derrls.f b/TESTING/LIN/derrls.f
index d885aab11..1823fb2c6 100644
--- a/TESTING/LIN/derrls.f
+++ b/TESTING/LIN/derrls.f
@@ -66,18 +66,18 @@ SUBROUTINE DERRLS( PATH, NUNIT )
 *  =====================================================================
 *
 *     .. Parameters ..
-      INTEGER            NMAX
-      PARAMETER          ( NMAX = 2 )
+      INTEGER            NMAX, LW, LIW
+      PARAMETER          ( NMAX = 2, LW = 1000, LIW = 30 )
 *     ..
 *     .. Local Scalars ..
       CHARACTER*2        C2
       INTEGER            INFO, IRNK
-      DOUBLE PRECISION   RCOND
+      DOUBLE PRECISION   NAN, ONE, RCOND
 *     ..
 *     .. Local Arrays ..
-      INTEGER            IP( NMAX )
+      INTEGER            IP( LIW )
       DOUBLE PRECISION   A( NMAX, NMAX ), B( NMAX, NMAX ), S( NMAX ),
-     $                   W( NMAX )
+     $                   W( LW )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -96,6 +96,9 @@ SUBROUTINE DERRLS( PATH, NUNIT )
       COMMON             / INFOC / INFOT, NOUT, OK, LERR
       COMMON             / SRNAMC / SRNAMT
 *     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          SQRT
+*     ..
 *     .. Executable Statements ..
 *
       NOUT = NUNIT
@@ -265,6 +268,26 @@ SUBROUTINE DERRLS( PATH, NUNIT )
          CALL DGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, 1, IP,
      $                INFO )
          CALL CHKXER( 'DGELSD', INFOT, NOUT, LERR, OK )
+*
+*        DGELSD must return INFO = 1, without calling XERBLA, when A
+*        contains a NaN: the NaN norm would otherwise be rejected by
+*        DLASCL inside DLALSD.
+*
+         ONE = 1.0D+0
+         NAN = SQRT( -ONE )
+         A( 2, 2 ) = NAN
+         B( 1, 1 ) = 1.0D+0
+         B( 2, 1 ) = 1.0D+0
+         RCOND = -1.0D+0
+         SRNAMT = 'DGELSD'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL DGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, LW, IP,
+     $                INFO )
+         IF( LERR .OR. INFO.NE.1 ) THEN
+            WRITE( NOUT, FMT = 9999 )INFO
+            OK = .FALSE.
+         END IF
       END IF
 *
 *     Print a summary line.
@@ -272,6 +295,9 @@ SUBROUTINE DERRLS( PATH, NUNIT )
       CALL ALAESM( PATH, OK, NOUT )
 *
       RETURN
+*
+ 9999 FORMAT( ' *** DGELSD on a matrix with a NaN returned INFO = ', I6,
+     $      ' instead of 1 ***' )
 *
 *     End of DERRLS
 *
diff --git a/TESTING/LIN/serrls.f b/TESTING/LIN/serrls.f
index e4c0bfe7f..9fa4f1cfc 100644
--- a/TESTING/LIN/serrls.f
+++ b/TESTING/LIN/serrls.f
@@ -66,18 +66,18 @@ SUBROUTINE SERRLS( PATH, NUNIT )
 *  =====================================================================
 *
 *     .. Parameters ..
-      INTEGER            NMAX
-      PARAMETER          ( NMAX = 2 )
+      INTEGER            NMAX, LW, LIW
+      PARAMETER          ( NMAX = 2, LW = 1000, LIW = 30 )
 *     ..
 *     .. Local Scalars ..
       CHARACTER*2        C2
       INTEGER            INFO, IRNK
-      REAL               RCOND
+      REAL               NAN, ONE, RCOND
 *     ..
 *     .. Local Arrays ..
-      INTEGER            IP( NMAX )
+      INTEGER            IP( LIW )
       REAL               A( NMAX, NMAX ), B( NMAX, NMAX ), S( NMAX ),
-     $                   W( NMAX )
+     $                   W( LW )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -96,6 +96,9 @@ SUBROUTINE SERRLS( PATH, NUNIT )
       COMMON             / INFOC / INFOT, NOUT, OK, LERR
       COMMON             / SRNAMC / SRNAMT
 *     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          SQRT
+*     ..
 *     .. Executable Statements ..
 *
       NOUT = NUNIT
@@ -265,6 +268,26 @@ SUBROUTINE SERRLS( PATH, NUNIT )
          CALL SGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, 1, IP,
      $                INFO )
          CALL CHKXER( 'SGELSD', INFOT, NOUT, LERR, OK )
+*
+*        SGELSD must return INFO = 1, without calling XERBLA, when A
+*        contains a NaN: the NaN norm would otherwise be rejected by
+*        SLASCL inside SLALSD.
+*
+         ONE = 1.0E+0
+         NAN = SQRT( -ONE )
+         A( 2, 2 ) = NAN
+         B( 1, 1 ) = 1.0E+0
+         B( 2, 1 ) = 1.0E+0
+         RCOND = -1.0E+0
+         SRNAMT = 'SGELSD'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL SGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, LW, IP,
+     $                INFO )
+         IF( LERR .OR. INFO.NE.1 ) THEN
+            WRITE( NOUT, FMT = 9999 )INFO
+            OK = .FALSE.
+         END IF
       END IF
 *
 *     Print a summary line.
@@ -272,6 +295,9 @@ SUBROUTINE SERRLS( PATH, NUNIT )
       CALL ALAESM( PATH, OK, NOUT )
 *
       RETURN
+*
+ 9999 FORMAT( ' *** SGELSD on a matrix with a NaN returned INFO = ', I6,
+     $      ' instead of 1 ***' )
 *
 *     End of SERRLS
 *
diff --git a/TESTING/LIN/zerrls.f b/TESTING/LIN/zerrls.f
index 2e7b7bcb7..12deae0f4 100644
--- a/TESTING/LIN/zerrls.f
+++ b/TESTING/LIN/zerrls.f
@@ -66,18 +66,18 @@ SUBROUTINE ZERRLS( PATH, NUNIT )
 *  =====================================================================
 *
 *     .. Parameters ..
-      INTEGER            NMAX
-      PARAMETER          ( NMAX = 2 )
+      INTEGER            NMAX, LW, LIW
+      PARAMETER          ( NMAX = 2, LW = 1000, LIW = 30 )
 *     ..
 *     .. Local Scalars ..
       CHARACTER*2        C2
       INTEGER            INFO, IRNK
-      DOUBLE PRECISION   RCOND
+      DOUBLE PRECISION   NAN, ONE, RCOND
 *     ..
 *     .. Local Arrays ..
-      INTEGER            IP( NMAX )
-      DOUBLE PRECISION   RW( NMAX ), S( NMAX )
-      COMPLEX*16         A( NMAX, NMAX ), B( NMAX, NMAX ), W( NMAX )
+      INTEGER            IP( LIW )
+      DOUBLE PRECISION   RW( LW ), S( NMAX )
+      COMPLEX*16         A( NMAX, NMAX ), B( NMAX, NMAX ), W( LW )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -96,6 +96,9 @@ SUBROUTINE ZERRLS( PATH, NUNIT )
       COMMON             / INFOC / INFOT, NOUT, OK, LERR
       COMMON             / SRNAMC / SRNAMT
 *     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          SQRT
+*     ..
 *     .. Executable Statements ..
 *
       NOUT = NUNIT
@@ -271,6 +274,26 @@ SUBROUTINE ZERRLS( PATH, NUNIT )
          CALL ZGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, 1, RW, IP,
      $                INFO )
          CALL CHKXER( 'ZGELSD', INFOT, NOUT, LERR, OK )
+*
+*        ZGELSD must return INFO = 1, without calling XERBLA, when A
+*        contains a NaN: the NaN norm would otherwise be rejected by
+*        DLASCL inside ZLALSD.
+*
+         ONE = 1.0D+0
+         NAN = SQRT( -ONE )
+         A( 2, 2 ) = NAN
+         B( 1, 1 ) = ( 1.0D+0, 0.0D+0 )
+         B( 2, 1 ) = ( 1.0D+0, 0.0D+0 )
+         RCOND = -1.0D+0
+         SRNAMT = 'ZGELSD'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL ZGELSD( 2, 2, 1, A, 2, B, 2, S, RCOND, IRNK, W, LW, RW,
+     $                IP, INFO )
+         IF( LERR .OR. INFO.NE.1 ) THEN
+            WRITE( NOUT, FMT = 9999 )INFO
+            OK = .FALSE.
+         END IF
       END IF
 *
 *     Print a summary line.
@@ -278,6 +301,9 @@ SUBROUTINE ZERRLS( PATH, NUNIT )
       CALL ALAESM( PATH, OK, NOUT )
 *
       RETURN
+*
+ 9999 FORMAT( ' *** ZGELSD on a matrix with a NaN returned INFO = ', I6,
+     $      ' instead of 1 ***' )
 *
 *     End of ZERRLS
 *