diff --git a/archive-tar.c b/archive-tar.c
index 7ea4e90814..55682404d5 100644
--- a/archive-tar.c
+++ b/archive-tar.c
@@ -25,8 +25,13 @@ static int write_tar_filter_archive(const struct archiver *ar,
  *
  * Likewise for the mtime (which happens to use a buffer of the same size).
  */
+#if ULONG_MAX == 0xFFFFFFFF
+#define USTAR_MAX_SIZE ULONG_MAX
+#define USTAR_MAX_MTIME ULONG_MAX
+#else
 #define USTAR_MAX_SIZE 077777777777UL
 #define USTAR_MAX_MTIME 077777777777UL
+#endif
 
 /* writes out the whole block, but only if it is full */
 static void write_if_needed(void)
diff --git a/t/t5000-tar-tree.sh b/t/t5000-tar-tree.sh
index 96d208da25..80b2387341 100755
--- a/t/t5000-tar-tree.sh
+++ b/t/t5000-tar-tree.sh
@@ -347,7 +347,7 @@ test_lazy_prereq TAR_HUGE '
 	test_cmp expect actual
 '
 
-test_expect_success 'set up repository with huge blob' '
+test_expect_success LONG_IS_64BIT 'set up repository with huge blob' '
 	obj_d=19 &&
 	obj_f=f9c8273ec45a8938e6999cb59b3ff66739902a &&
 	obj=${obj_d}${obj_f} &&
@@ -360,7 +360,7 @@ test_expect_success 'set up repository with huge blob' '
 
 # We expect git to die with SIGPIPE here (otherwise we
 # would generate the whole 64GB).
-test_expect_success 'generate tar with huge size' '
+test_expect_success LONG_IS_64BIT 'generate tar with huge size' '
 	{
 		git archive HEAD
 		echo $? >exit-code
@@ -369,13 +369,13 @@ test_expect_success 'generate tar with huge size' '
 	test_cmp expect exit-code
 '
 
-test_expect_success TAR_HUGE 'system tar can read our huge size' '
+test_expect_success TAR_HUGE,LONG_IS_64BIT 'system tar can read our huge size' '
 	echo 68719476737 >expect &&
 	tar_info huge.tar | cut -d" " -f1 >actual &&
 	test_cmp expect actual
 '
 
-test_expect_success 'set up repository with far-future commit' '
+test_expect_success LONG_IS_64BIT 'set up repository with far-future commit' '
 	rm -f .git/index &&
 	echo content >file &&
 	git add file &&
@@ -383,11 +383,11 @@ test_expect_success 'set up repository with far-future commit' '
 		git commit -m "tempori parendum"
 '
 
-test_expect_success 'generate tar with future mtime' '
+test_expect_success LONG_IS_64BIT 'generate tar with future mtime' '
 	git archive HEAD >future.tar
 '
 
-test_expect_success TAR_HUGE 'system tar can read our future mtime' '
+test_expect_success TAR_HUGE,LONG_IS_64BIT 'system tar can read our future mtime' '
 	echo 4147 >expect &&
 	tar_info future.tar | cut -d" " -f2 >actual &&
 	test_cmp expect actual