diff --git a/elf/Makefile b/elf/Makefile
index 3f3e711dd2..3ede79dc69 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -544,7 +544,20 @@ endif
 ifeq ($(have-dt-relr),yes)
 tests += \
   tst-relr \
+  tst-relr2 \
+  tst-relr3 \
+  tst-relr4 \
 # tests
+modules-names-dt-relr = \
+  tst-relr-mod2 \
+  tst-relr-mod3a \
+  tst-relr-mod3b \
+  tst-relr-mod4a \
+  tst-relr-mod4b \
+# modules-names-dt-relr
+modules-names += $(modules-names-dt-relr)
+# These shared libraries have special build rules.
+modules-names-nobuild += $(modules-names-dt-relr)
 ifeq ($(have-fpie),yes)
 tests += \
   tst-relr-pie \
@@ -603,7 +616,7 @@ test-extras += \
   tst-tlsmod17a \
   tst-tlsmod18a \
   # test-extras
-modules-names = \
+modules-names += \
   circlemod1 \
   circlemod1a \
   circlemod2 \
@@ -973,7 +986,7 @@ extra-test-objs += $(addsuffix .os,$(strip $(modules-names)))
 
 # filtmod1.so, tst-big-note-lib.so, tst-ro-dynamic-mod.so have special
 # rules.
-modules-names-nobuild := filtmod1 tst-big-note-lib tst-ro-dynamic-mod \
+modules-names-nobuild += filtmod1 tst-big-note-lib tst-ro-dynamic-mod \
 			 tst-audit24bmod1 tst-audit24bmod2
 
 tests += $(tests-static)
@@ -2768,3 +2781,50 @@ $(objpfx)check-tst-relr-pie.out: $(objpfx)tst-relr-pie
 		| sed -ne '/required from libc.so/,$$ p' \
 		| grep GLIBC_ABI_DT_RELR > $@; \
 	$(evaluate-test)
+
+# The test checks if a DT_RELR shared library without DT_NEEDED works as
+# intended, so it uses an explicit link rule.
+$(objpfx)tst-relr2: $(objpfx)tst-relr-mod2.so
+$(objpfx)tst-relr-mod2.so: $(objpfx)tst-relr-mod2.os
+	$(LINK.o) -nostdlib -nostartfiles -Wl,-z,pack-relative-relocs \
+	$(LDFLAGS-soname-fname) \
+	-shared -o $@.new $(filter-out $(map-file),$^)
+	$(call after-link,$@.new)
+	mv -f $@.new $@
+
+# The test checks if a DT_RELR shared library without DT_VERNEED works as
+# intended, so it uses an explicit link rule.
+$(objpfx)tst-relr3: $(objpfx)tst-relr-mod3a.so
+$(objpfx)tst-relr-mod3b.so: $(objpfx)tst-relr-mod3b.os
+	$(LINK.o) -nostdlib -nostartfiles -Wl,-z,pack-relative-relocs \
+	$(LDFLAGS-soname-fname) \
+	-shared -o $@.new $(filter-out $(map-file),$^)
+	$(call after-link,$@.new)
+	mv -f $@.new $@
+
+$(objpfx)tst-relr-mod3a.so: $(objpfx)tst-relr-mod3a.os \
+  $(objpfx)tst-relr-mod3b.so
+	$(LINK.o) -nostdlib -nostartfiles -Wl,-z,pack-relative-relocs \
+	$(LDFLAGS-soname-fname) \
+	-shared -o $@.new $(filter-out $(map-file),$^)
+	$(call after-link,$@.new)
+	mv -f $@.new $@
+
+# The test checks if a DT_RELR shared library without libc.so on DT_NEEDED
+# works as intended, so it uses an explicit link rule.
+$(objpfx)tst-relr4: $(objpfx)tst-relr-mod4a.so
+$(objpfx)tst-relr-mod4b.so: $(objpfx)tst-relr-mod4b.os
+	$(LINK.o) -nostdlib -nostartfiles -Wl,-z,pack-relative-relocs \
+	$(LDFLAGS-soname-fname) \
+	-Wl,--version-script=tst-relr-mod4b.map \
+	-shared -o $@.new $(filter-out $(map-file),$^)
+	$(call after-link,$@.new)
+	mv -f $@.new $@
+
+$(objpfx)tst-relr-mod4a.so: $(objpfx)tst-relr-mod4a.os \
+  $(objpfx)tst-relr-mod4b.so
+	$(LINK.o) -nostdlib -nostartfiles -Wl,-z,pack-relative-relocs \
+	$(LDFLAGS-soname-fname) \
+	-shared -o $@.new $(filter-out $(map-file),$^)
+	$(call after-link,$@.new)
+	mv -f $@.new $@
diff --git a/elf/tst-relr-mod2.c b/elf/tst-relr-mod2.c
new file mode 100644
index 0000000000..dc0a63365c
--- /dev/null
+++ b/elf/tst-relr-mod2.c
@@ -0,0 +1,46 @@
+/* Test for DT_RELR in a shared library without DT_NEEDED.
+   Copyright (C) 2022 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>
+
+static int o, x;
+
+#define ELEMS O O O O O O O O X X X X X X X O O X O O X X X E X E E O X O E
+#define E 0,
+
+#define O &o,
+#define X &x,
+void *arr[] = { ELEMS };
+#undef O
+#undef X
+
+#define O 1,
+#define X 2,
+static char val[] = { ELEMS };
+
+int
+foo (void)
+{
+  int err = 0;
+  for (int i = 0; i < array_length (arr); i++)
+    if (!((arr[i] == 0 && val[i] == 0)
+	  || (arr[i] == &o && val[i] == 1)
+	  || (arr[i] == &x && val[i] == 2)))
+      err++;
+  return err;
+}
diff --git a/elf/tst-relr-mod3a.c b/elf/tst-relr-mod3a.c
new file mode 100644
index 0000000000..d1621c91b1
--- /dev/null
+++ b/elf/tst-relr-mod3a.c
@@ -0,0 +1,49 @@
+/* Test for DT_RELR in a shared library without DT_VERNEED.
+   Copyright (C) 2022 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>
+
+static int o, x;
+
+#define ELEMS O O O O O O O O X X X X X X X O O X O O X X X E X E E O X O E
+#define E 0,
+
+#define O &o,
+#define X &x,
+void *arr[] = { ELEMS };
+#undef O
+#undef X
+
+#define O 1,
+#define X 2,
+static char val[] = { ELEMS };
+
+extern void bar (void);
+
+int
+foo (void)
+{
+  int err = 0;
+  for (int i = 0; i < array_length (arr); i++)
+    if (!((arr[i] == 0 && val[i] == 0)
+	  || (arr[i] == &o && val[i] == 1)
+	  || (arr[i] == &x && val[i] == 2)))
+      err++;
+  bar ();
+  return err;
+}
diff --git a/elf/tst-relr-mod3b.c b/elf/tst-relr-mod3b.c
new file mode 100644
index 0000000000..544cb4bc05
--- /dev/null
+++ b/elf/tst-relr-mod3b.c
@@ -0,0 +1,22 @@
+/* Test for DT_RELR in a shared library without DT_VERNEED.
+   Copyright (C) 2022 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/>.  */
+
+void
+bar (void)
+{
+}
diff --git a/elf/tst-relr-mod4a.c b/elf/tst-relr-mod4a.c
new file mode 100644
index 0000000000..e1bfebd4ac
--- /dev/null
+++ b/elf/tst-relr-mod4a.c
@@ -0,0 +1,19 @@
+/* Test for DT_RELR in a shared library without libc.so on DT_NEEDED.
+   Copyright (C) 2022 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 "tst-relr-mod3a.c"
diff --git a/elf/tst-relr-mod4b.c b/elf/tst-relr-mod4b.c
new file mode 100644
index 0000000000..617dff79c3
--- /dev/null
+++ b/elf/tst-relr-mod4b.c
@@ -0,0 +1,19 @@
+/* Test for DT_RELR in a shared library without libc.so on DT_NEEDED.
+   Copyright (C) 2022 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 "tst-relr-mod3b.c"
diff --git a/elf/tst-relr-mod4b.map b/elf/tst-relr-mod4b.map
new file mode 100644
index 0000000000..7f02247262
--- /dev/null
+++ b/elf/tst-relr-mod4b.map
@@ -0,0 +1,3 @@
+DT_RELR {
+  global: bar;
+};
diff --git a/elf/tst-relr2.c b/elf/tst-relr2.c
new file mode 100644
index 0000000000..10d77f1791
--- /dev/null
+++ b/elf/tst-relr2.c
@@ -0,0 +1,27 @@
+/* Test for DT_RELR in a shared library without DT_NEEDED.
+   Copyright (C) 2022 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/>.  */
+
+extern int foo (void);
+
+static int
+do_test (void)
+{
+  return foo ();
+}
+
+#include <support/test-driver.c>
diff --git a/elf/tst-relr3.c b/elf/tst-relr3.c
new file mode 100644
index 0000000000..69106cf7b7
--- /dev/null
+++ b/elf/tst-relr3.c
@@ -0,0 +1,27 @@
+/* Test for DT_RELR in a shared library without libc.so on DT_NEEDED.
+   Copyright (C) 2022 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/>.  */
+
+extern int foo (void);
+
+static int
+do_test (void)
+{
+  return foo ();
+}
+
+#include <support/test-driver.c>
diff --git a/elf/tst-relr4.c b/elf/tst-relr4.c
new file mode 100644
index 0000000000..19a75013f8
--- /dev/null
+++ b/elf/tst-relr4.c
@@ -0,0 +1 @@
+#include "tst-relr3.c"
