diff --git a/elf/Makefile b/elf/Makefile
index d3e909637a..3241cb6046 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -224,7 +224,7 @@ tests += restest1 preloadtest loadfail multiload origtest resolvfail \
 	 tst-single_threaded tst-single_threaded-pthread \
 	 tst-tls-ie tst-tls-ie-dlmopen argv0test \
 	 tst-glibc-hwcaps tst-glibc-hwcaps-prepend tst-glibc-hwcaps-mask \
-	 tst-tls20 tst-dlmopen-dlerror
+	 tst-tls20 tst-tls21 tst-dlmopen-dlerror
 #	 reldep9
 tests-internal += loadtest unload unload2 circleload1 \
 	 neededtest neededtest2 neededtest3 neededtest4 \
@@ -346,7 +346,7 @@ modules-names = testobj1 testobj2 testobj3 testobj4 testobj5 testobj6 \
 		libmarkermod2-1 libmarkermod2-2 \
 		libmarkermod3-1 libmarkermod3-2 libmarkermod3-3 \
 		libmarkermod4-1 libmarkermod4-2 libmarkermod4-3 libmarkermod4-4 \
-		tst-tls20mod-bad tst-dlmopen-dlerror-mod \
+		tst-tls20mod-bad tst-tls21mod tst-dlmopen-dlerror-mod \
 
 # Most modules build with _ISOMAC defined, but those filtered out
 # depend on internal headers.
@@ -1939,3 +1939,8 @@ tst-tls20mod-bad.so-no-z-defs = yes
 $(objpfx)tst-tls20: $(libdl) $(shared-thread-library)
 $(objpfx)tst-tls20.out: $(objpfx)tst-tls20mod-bad.so \
 			$(tst-tls-many-dynamic-modules:%=$(objpfx)%.so)
+
+# Reuses tst-tls-many-dynamic-modules
+$(objpfx)tst-tls21: $(libdl) $(shared-thread-library)
+$(objpfx)tst-tls21.out: $(objpfx)tst-tls21mod.so
+$(objpfx)tst-tls21mod.so: $(tst-tls-many-dynamic-modules:%=$(objpfx)%.so)
diff --git a/elf/tst-tls21.c b/elf/tst-tls21.c
new file mode 100644
index 0000000000..560bf5813a
--- /dev/null
+++ b/elf/tst-tls21.c
@@ -0,0 +1,68 @@
+/* Test concurrent dlopen and pthread_create: BZ 19329.
+   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
+   <http://www.gnu.org/licenses/>.  */
+
+#include <dlfcn.h>
+#include <pthread.h>
+#include <stdio.h>
+#include <stdatomic.h>
+#include <support/xdlfcn.h>
+#include <support/xthread.h>
+
+#define THREADS 10000
+
+static atomic_int done;
+
+static void *
+start (void *a)
+{
+  /* Load a module with many dependencies that each have TLS.  */
+  xdlopen ("tst-tls21mod.so", RTLD_LAZY);
+  atomic_store_explicit (&done, 1, memory_order_release);
+  return 0;
+}
+
+static void *
+nop (void *a)
+{
+  return 0;
+}
+
+static int
+do_test (void)
+{
+  pthread_t t1, t2;
+  int i;
+
+  /* Load a module with lots of dependencies and TLS.  */
+  t1 = xpthread_create (0, start, 0);
+
+  /* Concurrently create lots of threads until dlopen is observably done.  */
+  for (i = 0; i < THREADS; i++)
+    {
+      if (atomic_load_explicit (&done, memory_order_acquire) != 0)
+	break;
+      t2 = xpthread_create (0, nop, 0);
+      xpthread_join (t2);
+    }
+
+  xpthread_join (t1);
+  printf ("threads created during dlopen: %d\n", i);
+  return 0;
+}
+
+#include <support/test-driver.c>
diff --git a/elf/tst-tls21mod.c b/elf/tst-tls21mod.c
new file mode 100644
index 0000000000..206ece4fb3
--- /dev/null
+++ b/elf/tst-tls21mod.c
@@ -0,0 +1 @@
+int __thread x;