diff --git a/t/op/require_errors.t b/t/op/require_errors.t
index 2d7c587e11e69..ec8d4091fdefe 100644
--- a/t/op/require_errors.t
+++ b/t/op/require_errors.t
@@ -177,10 +177,15 @@ SKIP: {
     push @INC, '../lib';
     require Cwd;
     require File::Spec::Functions;
+    require Config;
     if ($^O eq 'cygwin') {
         require Win32;
     }
 
+    my $cwd = Cwd::getcwd();
+    skip "AFS", 2
+      if $Config::Config{afs} eq "true" && $cwd && $cwd =~ /^\Q$Config::Config{afsroot}/;
+
     # Going to try to switch away from root.  Might not work.
     # (stolen from t/op/stat.t)
     my $olduid = $>;
@@ -196,9 +201,9 @@ SKIP: {
 
     SKIP: {
         skip "Can't make the path absolute", 1
-            if !defined(Cwd::getcwd());
+            if !defined $cwd;
 
-        my $file = File::Spec::Functions::catfile(Cwd::getcwd(), $mod_file);
+        my $file = File::Spec::Functions::catfile($cwd, $mod_file);
         eval {
             require($file);
         };
diff --git a/t/op/stat.t b/t/op/stat.t
index b391dd0e7c836..f69fa5cfa890d 100644
--- a/t/op/stat.t
+++ b/t/op/stat.t
@@ -548,7 +548,10 @@ SKIP: {
 }
 
 # [perl #4253]
+SKIP:
 {
+    skip "AFS", 1
+      if $Config{afs} eq "true" && ($Curdir eq '.' || $Curdir =~ /^\Q$Config{afsroot}/);
     ok(open(F, ">", $tmpfile), 'can create temp file');
     close F;
     chmod 0077, $tmpfile;