diff --git a/gprof/testsuite/Makefile.am b/gprof/testsuite/Makefile.am
index 0c80b12e6e4..7ab1c2ea6b7 100644
--- a/gprof/testsuite/Makefile.am
+++ b/gprof/testsuite/Makefile.am
@@ -37,7 +37,9 @@ tst-gmon-gprof.out: tst-gmon$(EXEEXT) $(GPROF)
 
 check_SCRIPTS += tst-gmon-gprof-l.sh
 check_DATA += tst-gmon-gprof-l.out
-tst-gmon-gprof-l.out: tst-gmon$(EXEEXT) $(GPROF)
+# Run tst-gmon-gprof-l.sh after tst-gmon-gprof.sh to avoid the race
+# condition since they both generate gmon.out.
+tst-gmon-gprof-l.out: tst-gmon$(EXEEXT) $(GPROF) tst-gmon-gprof.out
 	$(srcdir)/tst-gmon-gprof-l.sh $(GPROF) tst-gmon$(EXEEXT)
 
 endif NATIVE
diff --git a/gprof/testsuite/Makefile.in b/gprof/testsuite/Makefile.in
index 2ac5f241012..ab8a2cbb16e 100644
--- a/gprof/testsuite/Makefile.in
+++ b/gprof/testsuite/Makefile.in
@@ -884,7 +884,9 @@ uninstall-am:
 @NATIVE_TRUE@	$(LINK) tst-gmon.$(OBJEXT)
 @NATIVE_TRUE@tst-gmon-gprof.out: tst-gmon$(EXEEXT) $(GPROF)
 @NATIVE_TRUE@	$(srcdir)/tst-gmon-gprof.sh $(GPROF) tst-gmon$(EXEEXT)
-@NATIVE_TRUE@tst-gmon-gprof-l.out: tst-gmon$(EXEEXT) $(GPROF)
+# Run tst-gmon-gprof-l.sh after tst-gmon-gprof.sh to avoid the race
+# condition since they both generate gmon.out.
+@NATIVE_TRUE@tst-gmon-gprof-l.out: tst-gmon$(EXEEXT) $(GPROF) tst-gmon-gprof.out
 @NATIVE_TRUE@	$(srcdir)/tst-gmon-gprof-l.sh $(GPROF) tst-gmon$(EXEEXT)
 
 # Tell versions [3.59,3.63) of GNU make to not export all variables.