diff --git a/sysdeps/unix/sysv/linux/Makefile b/sysdeps/unix/sysv/linux/Makefile
index be6fe08ac2..74a8d865b2 100644
--- a/sysdeps/unix/sysv/linux/Makefile
+++ b/sysdeps/unix/sysv/linux/Makefile
@@ -237,8 +237,8 @@ sysdep_routines += cmsg_nxthdr
 CFLAGS-recvmmsg.c = -fexceptions -fasynchronous-unwind-tables
 CFLAGS-sendmmsg.c = -fexceptions -fasynchronous-unwind-tables
 
-tests += tst-recvmsg
-tests-time64 += tst-recvmsg-time64
+tests += tst-recvmsg tst-recvmmsg
+tests-time64 += tst-recvmsg-time64 tst-recvmmsg-time64
 
 tests-special += $(objpfx)tst-socket-consts.out
 $(objpfx)tst-socket-consts.out: ../sysdeps/unix/sysv/linux/tst-socket-consts.py
diff --git a/sysdeps/unix/sysv/linux/tst-recvmmsg-time64.c b/sysdeps/unix/sysv/linux/tst-recvmmsg-time64.c
new file mode 100644
index 0000000000..7b9b1bea03
--- /dev/null
+++ b/sysdeps/unix/sysv/linux/tst-recvmmsg-time64.c
@@ -0,0 +1 @@
+#include "tst-recvmmsg.c"
diff --git a/sysdeps/unix/sysv/linux/tst-recvmmsg.c b/sysdeps/unix/sysv/linux/tst-recvmmsg.c
new file mode 100644
index 0000000000..012b364434
--- /dev/null
+++ b/sysdeps/unix/sysv/linux/tst-recvmmsg.c
@@ -0,0 +1,185 @@
+/* Check recvmmsg timestamp support.
+   Copyright (C) 2021 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
+   <https://www.gnu.org/licenses/>.  */
+
+#include <array_length.h>
+#include <arpa/inet.h>
+#include <errno.h>
+#include <string.h>
+#include <stdio.h>
+#include <support/check.h>
+#include <support/support.h>
+#include <support/xunistd.h>
+#include <support/xsocket.h>
+#include <sys/mman.h>
+
+/* Some extra space added for ancillary data, it might be used to convert
+   32-bit timestamp to 64-bit for _TIME_BITS=64 on older kernels.  */
+static const int slack[] = { 0, 4, 8, 16, 32, 64 };
+
+static size_t pagesize;
+
+static int
+do_test_send (const struct sockaddr_in *addr, int nmsgs)
+{
+  int s = xsocket (AF_INET, SOCK_DGRAM | SOCK_CLOEXEC, 0);
+  xconnect (s, (const struct sockaddr *) addr, sizeof (*addr));
+
+  for (int i = 0; i < nmsgs; i++)
+    xsendto (s, &i, sizeof (i), 0, (const struct sockaddr *) addr,
+	     sizeof (*addr));
+
+  return 0;
+}
+
+#define NMSGS 5
+
+static void
+do_recvmmsg (int s, bool support_64_timestamp, void *cmsg[], size_t slack,
+	     size_t tsize)
+{
+  /* A timestamp is expected if 32-bit timestamp are used (support in every
+     configuration) or if underlying kernel support 64-bit timestamps.
+     Otherwise recvmsg will need extra space do add the 64-bit timestamp.  */
+  bool exp_timestamp;
+  if (sizeof (time_t) == 4 || support_64_timestamp)
+    exp_timestamp = true;
+  else
+    exp_timestamp = slack >= CMSG_SPACE (tsize);
+
+  int msg[5];
+  struct iovec iov[NMSGS];
+  for (int i = 0; i < NMSGS; i++)
+    {
+      iov[i].iov_base = &msg[i];
+      iov[i].iov_len = sizeof (msg[i]);
+    }
+  struct mmsghdr msghdr[NMSGS];
+  size_t msgs = CMSG_SPACE (tsize + slack);
+  for (int i = 0; i < NMSGS; i++)
+    {
+      msghdr[i].msg_hdr.msg_name = NULL;
+      msghdr[i].msg_hdr.msg_namelen = 0;
+      msghdr[i].msg_hdr.msg_iov = &iov[i];
+      msghdr[i].msg_hdr.msg_iovlen = 1;
+      msghdr[i].msg_hdr.msg_controllen = msgs,
+      msghdr[i].msg_hdr.msg_control = cmsg[i] != NULL
+				      ? cmsg[i] + pagesize - msgs : NULL;
+    }
+  
+  TEST_COMPARE (recvmmsg (s, msghdr, NMSGS, 0, NULL), NMSGS);
+  for (int i = 0; i < NMSGS; i++)
+    {
+      if (msghdr[i].msg_len == 0)
+	continue;
+
+      TEST_COMPARE (msg[i], i);
+
+      int timestamp = false;
+      for (struct cmsghdr *cmsg = CMSG_FIRSTHDR (&msghdr[i].msg_hdr);
+	   cmsg != NULL;
+	   cmsg = CMSG_NXTHDR (&msghdr[i].msg_hdr, cmsg))
+	{
+	  if (cmsg->cmsg_level != SOL_SOCKET)
+	    continue;
+	  if (cmsg->cmsg_type == SCM_TIMESTAMP
+	      && cmsg->cmsg_len == CMSG_LEN (sizeof (struct timeval)))
+	    {
+	      struct timeval tv;
+	      memcpy (&tv, CMSG_DATA (cmsg), sizeof (tv));
+	      printf ("SCM_TIMESTAMP:   {%jd, %jd}\n", (intmax_t)tv.tv_sec,
+		      (intmax_t)tv.tv_usec);
+	      timestamp = true;
+	    }
+	  else if (cmsg->cmsg_type == SCM_TIMESTAMPNS
+		   && cmsg->cmsg_len == CMSG_LEN (sizeof (struct timespec)))
+	    {
+	      struct timespec ts;
+	      memcpy (&ts, CMSG_DATA (cmsg), sizeof (ts));
+	      printf ("SCM_TIMESTAMPNS: {%jd, %jd}\n", (intmax_t)ts.tv_sec,
+		      (intmax_t)ts.tv_nsec);
+	      timestamp = true;
+	    }
+	}
+
+      /* If there is not timestamp in the ancilliary data, recvmsg should set
+	 the flag inidcating it.  */
+      if (exp_timestamp && !timestamp)
+	TEST_VERIFY (msghdr[i].msg_hdr.msg_flags & MSG_TRUNC);
+      else
+	TEST_COMPARE (exp_timestamp, timestamp);
+    }
+}
+
+static int
+do_test (void)
+{
+  int srv = xsocket (AF_INET, SOCK_DGRAM, 0);
+  struct sockaddr_in srv_addr =
+    {
+      .sin_family = AF_INET,
+      .sin_addr = {.s_addr = htonl (INADDR_LOOPBACK) },
+    };
+  xbind (srv, (struct sockaddr *) &srv_addr, sizeof (srv_addr));
+  {
+    socklen_t sa_len = sizeof (srv_addr);
+    xgetsockname (srv, (struct sockaddr *) &srv_addr, &sa_len);
+    TEST_VERIFY (sa_len == sizeof (srv_addr));
+  }
+
+  TEST_COMPARE (recvmmsg (-1, NULL, 0, 0, NULL), -1);
+  TEST_COMPARE (errno, EBADF);
+
+  /* Setup the ancillary data buffer with an extra page with PROT_NONE to
+     check the possible timestamp conversion on some systems.  */
+  pagesize = sysconf (_SC_PAGESIZE);
+  if (pagesize == -1)
+    FAIL_EXIT1 ("sysconf (_SC_PAGESIZE): %m\n");
+  void *msgbuf[NMSGS];
+  for (int i = 0; i < NMSGS; i++)
+    {
+      msgbuf[i] = xmmap (0, 2 * pagesize, PROT_NONE,
+			 MAP_ANONYMOUS | MAP_PRIVATE, -1);
+      xmprotect (msgbuf[i], pagesize, PROT_READ | PROT_WRITE);
+    }
+
+  /* If underlying kernel does not support   */
+  bool support_64_timestamp = support_socket_time64_timestamp (srv);
+
+  /* Enable the timestamp using struct timeval precision.  */
+  xsetsockopt (srv, SOL_SOCKET, SO_TIMESTAMP, &(int){1}, sizeof (int));
+  for (int s = 0; s < array_length (slack); s++)
+    {
+      do_test_send (&srv_addr, NMSGS);
+      do_recvmmsg (srv, support_64_timestamp, msgbuf, slack[s],
+		   sizeof (struct timeval));
+    }
+
+  /* Now enable timestamp using a higher precision, it overwrites the previous
+     precision.  */
+  xsetsockopt (srv, SOL_SOCKET, SO_TIMESTAMPNS, &(int){1}, sizeof (int));
+  for (int s = 0; s < array_length (slack); s++)
+    {
+      do_test_send (&srv_addr, NMSGS);
+      do_recvmmsg (srv, support_64_timestamp, msgbuf, slack[s],
+		   sizeof (struct timespec));
+    }
+
+  return 0;
+}
+
+#include <support/test-driver.c>
