diff --git a/gdb/testsuite/gdb.base/auxv.exp b/gdb/testsuite/gdb.base/auxv.exp
index da10f05..e1b8cb0 100644
--- a/gdb/testsuite/gdb.base/auxv.exp
+++ b/gdb/testsuite/gdb.base/auxv.exp
@@ -42,8 +42,19 @@ set coredir "${objdir}/${subdir}/coredir.[getpid]"
 file mkdir $coredir
 set core_works [expr [isnative] && ! [is_remote target]]
 
-# Run GDB on the test program up to where it will dump core.
+global gdb_prompt
+
+gdb_exit
+gdb_start
+send_gdb "shell ulimit -c\n"
+gdb_expect {
+    -re "0\r\n$gdb_prompt $" {
+        warning "ulimit -c is 0, disabling core tests"
+        set core_works 0
+    }
+}
 
+# Run GDB on the test program up to where it will dump core.
 gdb_exit
 gdb_start
 gdb_reinitialize_dir $srcdir/$subdir
@@ -51,11 +62,9 @@ gdb_load ${binfile}
 gdb_test_no_output "set print sevenbit-strings"
 gdb_test_no_output "set width 0"
 
-if {$core_works} {
-    if {[gdb_test "cd $coredir" ".*Working directory .*" \
-	     "cd to temporary directory for core dumps"]} {
-	set core_works 0
-    }
+if {[gdb_test "cd $coredir" ".*Working directory .*" \
+         "cd to temporary directory for core dumps"]} {
+    set core_works 0
 }
 
 if { ![runto_main] } then {
@@ -154,7 +163,7 @@ if {$core_works} {
 	pass $test
     } else {
 	set core_works 0
-	warning "can't generate a core file - core tests suppressed - check ulimit -c"
+	warning "can't generate a core file - core tests suppressed"
 	fail $test
     }
 } else {
diff --git a/gdb/testsuite/gdb.base/cond-eval-mode.exp b/gdb/testsuite/gdb.base/cond-eval-mode.exp
index dbbfc28..965c497 100644
--- a/gdb/testsuite/gdb.base/cond-eval-mode.exp
+++ b/gdb/testsuite/gdb.base/cond-eval-mode.exp
@@ -30,7 +30,7 @@ gdb_test_no_output $test_auto
 
 # If target-side condition evaluation is not supported, this warning will be
 # displayed.
-set warning "warning: Target does not support breakpoint condition evaluation.\r\nUsing GDB evaluation mode instead.\r\n"
+set warning "warning: Target does not support breakpoint condition evaluation.\r\nUsing host evaluation mode instead.\r\n"
 
 gdb_test_multiple $test_target $test_target {
     -re "$warning$gdb_prompt $" {
-- 
1.7.7.4