diff --git a/io/test-lfs.c b/io/test-lfs.c
index f7721a5995..52120e9bca 100644
--- a/io/test-lfs.c
+++ b/io/test-lfs.c
@@ -25,6 +25,7 @@
 #include <error.h>
 #include <errno.h>
 #include <sys/resource.h>
+#include <support/check.h>
 
 /* Prototype for our test function.  */
 extern void do_prepare (int argc, char *argv[]);
@@ -70,6 +71,8 @@ do_prepare (int argc, char *argv[])
       else
 	error (EXIT_FAILURE, errno, "cannot create temporary file");
     }
+  if (!support_descriptor_supports_holes (fd))
+    FAIL_UNSUPPORTED ("File %s does not support holes", name);
   add_temp_file (name);
 
   if (getrlimit64 (RLIMIT_FSIZE, &rlim) != 0)
diff --git a/io/tst-copy_file_range.c b/io/tst-copy_file_range.c
index 3d531a1937..e5b46f91db 100644
--- a/io/tst-copy_file_range.c
+++ b/io/tst-copy_file_range.c
@@ -739,7 +739,12 @@ do_test (void)
     *p = rand () >> 24;
 
   infd = create_temp_file ("tst-copy_file_range-in-", &infile);
-  xclose (create_temp_file ("tst-copy_file_range-out-", &outfile));
+  {
+    int outfd = create_temp_file ("tst-copy_file_range-out-", &outfile);
+    if (!support_descriptor_supports_holes (outfd))
+      FAIL_UNSUPPORTED ("File %s does not support holes", outfile);
+    xclose (outfd);
+  }
 
   /* Try to find a different directory from the default input/output
      file.  */
diff --git a/misc/tst-preadvwritev-common.c b/misc/tst-preadvwritev-common.c
index b59a3de465..4a5e53a140 100644
--- a/misc/tst-preadvwritev-common.c
+++ b/misc/tst-preadvwritev-common.c
@@ -17,6 +17,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <array_length.h>
+#include <stdbool.h>
 #include <stdio.h>
 #include <stdint.h>
 #include <errno.h>
@@ -26,10 +27,12 @@
 
 #include <support/check.h>
 #include <support/temp_file.h>
+#include <support/support.h>
 #include <support/xunistd.h>
 
 static char *temp_filename;
 static int temp_fd;
+static bool temp_fd_supports_holes;
 
 static int do_test (void);
 
@@ -39,6 +42,7 @@ do_prepare (int argc, char **argv)
   temp_fd = create_temp_file ("tst-preadvwritev.", &temp_filename);
   if (temp_fd == -1)
     FAIL_EXIT1 ("cannot create temporary file");
+  temp_fd_supports_holes = support_descriptor_supports_holes (temp_fd);
 }
 #define PREPARE do_prepare
 
diff --git a/misc/tst-preadvwritev64.c b/misc/tst-preadvwritev64.c
index b718da6be5..451d03e4a8 100644
--- a/misc/tst-preadvwritev64.c
+++ b/misc/tst-preadvwritev64.c
@@ -26,6 +26,12 @@ do_test (void)
 
   ret = do_test_with_offset (0);
 
+  if (!temp_fd_supports_holes)
+    {
+      puts ("warning: partial test due to lack of support for holes");
+      return ret;
+    }
+
   /* Create a sparse file larger than 4GB to check if offset is handled
      correctly in p{write,read}v64. */
   off_t base_offset = UINT32_MAX + 2048LL;
diff --git a/support/Makefile b/support/Makefile
index 652d2cdf69..9063046c23 100644
--- a/support/Makefile
+++ b/support/Makefile
@@ -43,6 +43,7 @@ libsupport-routines = \
   support_capture_subprocess \
   support_capture_subprocess_check \
   support_chroot \
+  support_descriptor_supports_holes \
   support_enter_mount_namespace \
   support_enter_network_namespace \
   support_format_address_family \
diff --git a/support/support.h b/support/support.h
index b61fe0735c..34ae6e10cd 100644
--- a/support/support.h
+++ b/support/support.h
@@ -65,6 +65,12 @@ void support_write_file_string (const char *path, const char *contents);
    the result).  */
 char *support_quote_blob (const void *blob, size_t length);
 
+/* Returns non-zero if the file descriptor is a regular file on a file
+   system which supports holes (that is, seeking and writing does not
+   allocate storage for the range of zeros).  FD must refer to a
+   regular file open for writing, and initially empty.  */
+int support_descriptor_supports_holes (int fd);
+
 /* Error-checking wrapper functions which terminate the process on
    error.  */
 
diff --git a/support/support_descriptor_supports_holes.c b/support/support_descriptor_supports_holes.c
new file mode 100644
index 0000000000..b04498664e
--- /dev/null
+++ b/support/support_descriptor_supports_holes.c
@@ -0,0 +1,80 @@
+/* Test for file system hole support.
+   Copyright (C) 2018 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <stdbool.h>
+#include <support.h>
+#include <support/check.h>
+#include <sys/stat.h>
+#include <xunistd.h>
+
+int
+support_descriptor_supports_holes (int fd)
+{
+  enum
+    {
+      /* Write offset for the enlarged file.  This value is arbitrary
+         and hopefully large enough to trigger the creation of holes.
+         We cannot use the file system block size as a reference here
+         because it is incorrect for network file systems.  */
+      write_offset = 16 * 1024 * 1024,
+
+      /* Our write may add this number of additional blocks.  */
+      block_headroom = 8,
+    };
+
+  struct stat64 st;
+  xfstat (fd, &st);
+  if (!S_ISREG (st.st_mode))
+    FAIL_EXIT1 ("descriptor %d does not refer to a regular file", fd);
+  if (st.st_size != 0)
+    FAIL_EXIT1 ("descriptor %d does not refer to an empty file", fd);
+  if (st.st_blocks > block_headroom)
+    FAIL_EXIT1 ("descriptor %d refers to a pre-allocated file (%lld blocks)",
+                fd, (long long int) st.st_blocks);
+
+  /* Write a single byte at the start of the file to compute the block
+     usage for a single byte.  */
+  xlseek (fd, 0, SEEK_SET);
+  char b = '@';
+  xwrite (fd, &b, 1);
+  /* Attempt to bypass delayed allocation.  */
+  TEST_COMPARE (fsync (fd), 0);
+  xfstat (fd, &st);
+  unsigned long long int block_limit = 2 * st.st_blocks + block_headroom;
+
+  /* Write a single byte at 16 megabytes.  */
+  xlseek (fd, write_offset, SEEK_SET);
+  xwrite (fd, &b, 1);
+  /* Attempt to bypass delayed allocation.  */
+  TEST_COMPARE (fsync (fd), 0);
+  xfstat (fd, &st);
+  bool supports_holes = st.st_blocks <= block_limit;
+
+  /* Also check that extending the file does not fill up holes.  */
+  xftruncate (fd, 2 * write_offset);
+  /* Attempt to bypass delayed allocation.  */
+  TEST_COMPARE (fsync (fd), 0);
+  xfstat (fd, &st);
+  supports_holes = supports_holes && st.st_blocks <= block_limit;
+
+  /* Return to a zero-length file.  */
+  xftruncate (fd, 0);
+  xlseek (fd, 0, SEEK_SET);
+
+  return supports_holes;
+}
diff --git a/sysdeps/unix/sysv/linux/tst-fallocate-common.c b/sysdeps/unix/sysv/linux/tst-fallocate-common.c
index a6ba403c62..bc54cf5134 100644
--- a/sysdeps/unix/sysv/linux/tst-fallocate-common.c
+++ b/sysdeps/unix/sysv/linux/tst-fallocate-common.c
@@ -41,6 +41,8 @@ do_prepare (int argc, char **argv)
   temp_fd = create_temp_file ("tst-fallocate.", &temp_filename);
   if (temp_fd == -1)
     FAIL_EXIT1 ("cannot create temporary file: %m");
+  if (!support_descriptor_supports_holes (temp_fd))
+    FAIL_UNSUPPORTED ("File %s does not support holes", temp_filename);
 }
 #define PREPARE do_prepare
 
diff --git a/timezone/tst-tzset.c b/timezone/tst-tzset.c
index 27f986b56d..744c583f7e 100644
--- a/timezone/tst-tzset.c
+++ b/timezone/tst-tzset.c
@@ -24,6 +24,7 @@
 #include <sys/resource.h>
 #include <time.h>
 #include <unistd.h>
+#include <support/check.h>
 
 #define TIMEOUT 5
 static int do_test (void);
@@ -38,6 +39,8 @@ create_tz_file (off64_t size)
   int fd = create_temp_file ("tst-tzset-", &path);
   if (fd < 0)
     exit (1);
+  if (!support_descriptor_supports_holes (fd))
+    FAIL_UNSUPPORTED ("File %s does not support holes", path);
 
   // Reopen for large-file support.
   close (fd);
