diff --git a/gdb/testsuite/ChangeLog b/gdb/testsuite/ChangeLog
index 117ab9bb53..3532ed3ed0 100644
--- a/gdb/testsuite/ChangeLog
+++ b/gdb/testsuite/ChangeLog
@@ -1,3 +1,10 @@
+2017-10-13  Pedro Alves  <palves@redhat.com>
+
+	* gdb.base/corefile.exp (corefile_test_run): Skip if gdb_protocol
+	is set.
+	(corefile_test_attach): Likewise.  Check can_spawn_for_attach
+	instead of is_remote.
+
 2017-10-13  Pedro Alves  <palves@redhat.com>
 
 	* gdb.base/remote.exp: Check gdb_protocol instead of is_remote.
diff --git a/gdb/testsuite/gdb.base/corefile.exp b/gdb/testsuite/gdb.base/corefile.exp
index 21b974fbbd..9be4aef7f4 100644
--- a/gdb/testsuite/gdb.base/corefile.exp
+++ b/gdb/testsuite/gdb.base/corefile.exp
@@ -188,6 +188,15 @@ gdb_test "core" "No core file now."
 proc corefile_test_run {} {
     global corefile gdb_prompt
 
+    # This test is trying to check whether the "run" command finds the
+    # default run target when already debugging a core, so it would
+    # fail on boards that set auto-connect-native-target off.  Since
+    # there's no real point in running the test but with the native
+    # target, it's easier to just skip elsewhere.
+    if {[target_info gdb_protocol] != ""} {
+	return
+    }
+
     gdb_test "core-file $corefile" "Core was generated by .*" "run: load core again"
     gdb_test "info files" "\r\nLocal core dump file:\r\n.*" "run: sanity check we see the core file"
 
@@ -244,7 +253,16 @@ gdb_exit
 proc corefile_test_attach {} {
     global binfile corefile gdb_prompt
 
-    if ![is_remote target] {
+    # This test is checking whether the "attach" command finds the
+    # default run target when already debugging a core, so it would
+    # fail on boards that set auto-connect-native-target off.  Since
+    # there's no real point in running the test but with the native
+    # target, it's easier to just skip elsewhere.
+    if {[target_info gdb_protocol] != ""} {
+	return
+    }
+
+    if [can_spawn_for_attach] {
 	set test "attach: spawn sleep"
 	set res [remote_spawn host "$binfile sleep"]
 	if { $res < 0 || $res == "" } {