diff --git a/test/TEST-07-PID1/test.sh b/test/TEST-07-PID1/test.sh
index b3421520f65..a5982e0183e 100755
--- a/test/TEST-07-PID1/test.sh
+++ b/test/TEST-07-PID1/test.sh
@@ -4,6 +4,9 @@ set -e
 
 TEST_DESCRIPTION="Tests for core PID1 functionality"
 
+# for testing PrivateNetwork=yes
+NSPAWN_ARGUMENTS="--capability=CAP_NET_ADMIN"
+
 # shellcheck source=test/test-functions
 . "${TEST_BASE_DIR:?}/test-functions"
 
diff --git a/test/units/testsuite-07.private-network.sh b/test/units/testsuite-07.private-network.sh
new file mode 100755
index 00000000000..37658f7d1cd
--- /dev/null
+++ b/test/units/testsuite-07.private-network.sh
@@ -0,0 +1,7 @@
+#!/usr/bin/env bash
+# SPDX-License-Identifier: LGPL-2.1-or-later
+set -eux
+set -o pipefail
+
+# For issue https://github.com/systemd/systemd/issues/29526
+systemd-run -p PrivateNetwork=yes --wait /bin/true