diff --git a/test/zdtm/static/Makefile b/test/zdtm/static/Makefile
index a3c1ccf4b..5a8a5f75c 100644
--- a/test/zdtm/static/Makefile
+++ b/test/zdtm/static/Makefile
@@ -184,6 +184,8 @@ TST_NOFILE	:=				\
 		stopped01			\
 		stopped02			\
 		stopped12			\
+		stopped03			\
+		stopped04			\
 		rtc				\
 		clean_mntns			\
 		mntns_rw_ro_rw			\
diff --git a/test/zdtm/static/stopped03.c b/test/zdtm/static/stopped03.c
new file mode 100644
index 000000000..85c7177f7
--- /dev/null
+++ b/test/zdtm/static/stopped03.c
@@ -0,0 +1,161 @@
+#include <signal.h>
+#include <sys/wait.h>
+#include <sys/mman.h>
+
+#include "zdtmtst.h"
+#include "lock.h"
+
+const char *test_doc = "Check, that stopped by SIGTSTP tasks are restored correctly";
+const char *test_author = "Yuriy Vasiliev <yuriy.vasiliev@openvz.org>";
+
+#define STOP_SIGNO SIGTSTP
+const char *stop_sigstr = "SIGTSTP";
+enum {
+	FUTEX_INITIALIZED = 0,
+	TEST_CRIU,
+	TEST_CHECK,
+	TEST_DONE,
+	TEST_EXIT,
+	TEST_EMERGENCY_ABORT,
+};
+
+struct shared {
+	futex_t fstate;
+	int status;
+	int code;
+} * sh;
+
+static int new_pgrp(void)
+{
+	siginfo_t infop;
+	int ret = 1;
+	pid_t pid;
+
+	/*
+	 * Set the PGID to avoid creating an orphaned process group,
+	 * which is not to be affected by terminal-generated stop signals.
+	 */
+	setpgid(0, 0);
+
+	pid = test_fork();
+	if (pid < 0)
+		goto err_cr;
+
+	if (pid == 0) {
+		/* wait for TEST_EXIT or TEST_EMERGENCY_ABORT*/
+		futex_wait_while_lt(&sh->fstate, TEST_EXIT);
+		exit(0);
+	}
+
+	if (kill(pid, STOP_SIGNO)) {
+		pr_perror("Unable to send %s", stop_sigstr);
+		goto err_cr;
+	}
+
+	if (waitid(P_PID, pid, &infop, WNOWAIT | WSTOPPED) < 0) {
+		pr_perror("Unable to waitid %d", pid);
+		goto err_cont;
+	}
+
+	sh->code = infop.si_code;
+	sh->status = infop.si_status;
+
+	/* Return the control back to MAIN worker to do C/R */
+	futex_set_and_wake(&sh->fstate, TEST_CRIU);
+	futex_wait_while_lt(&sh->fstate, TEST_CHECK);
+
+	infop.si_code = 0;
+	infop.si_status = 0;
+
+	if (waitid(P_PID, pid, &infop, WNOWAIT | WSTOPPED) < 0) {
+		pr_perror("Unable to waitid %d", pid);
+		goto err_cont;
+	}
+
+	sh->code = infop.si_code;
+	sh->status = infop.si_status;
+
+	futex_set_and_wake(&sh->fstate, TEST_DONE);
+	futex_wait_while_lt(&sh->fstate, TEST_EXIT);
+
+	ret = 0;
+err_cont:
+	kill(pid, SIGCONT);
+err_cr:
+	if (ret)
+		futex_set_and_wake(&sh->fstate, TEST_EMERGENCY_ABORT);
+	if (pid > 0)
+		wait(NULL);
+
+	return ret;
+}
+
+int main(int argc, char **argv)
+{
+	int fail = 0;
+	pid_t pid;
+
+	test_init(argc, argv);
+
+	sh = mmap(NULL, sizeof(struct shared), PROT_WRITE | PROT_READ, MAP_SHARED | MAP_ANONYMOUS, -1, 0);
+	if (sh == MAP_FAILED) {
+		pr_perror("Failed to alloc shared region");
+		return 1;
+	}
+
+	futex_set(&sh->fstate, FUTEX_INITIALIZED);
+
+	pid = test_fork();
+	if (pid < 0) {
+		fail = 1;
+		goto out;
+	}
+
+	if (pid == 0)
+		exit(new_pgrp());
+
+	/* Wait until pgrp is ready to C/R */
+	futex_wait_while_lt(&sh->fstate, TEST_CRIU);
+	if (futex_get(&sh->fstate) == TEST_EMERGENCY_ABORT) {
+		pr_err("Fail in child worker before C/R\n");
+		fail = 1;
+		goto out;
+	}
+
+	if (sh->code != CLD_STOPPED || sh->status != STOP_SIGNO) {
+		pr_err("Process is not in correct state before C/R."
+		       " Expected stop signo: %d. Get stop signo: %d\n",
+		       STOP_SIGNO, sh->status);
+		fail = 1;
+		goto out;
+	}
+
+	test_daemon();
+	test_waitsig();
+
+	futex_set_and_wake(&sh->fstate, TEST_CHECK);
+	futex_wait_while_lt(&sh->fstate, TEST_DONE);
+	if (futex_get(&sh->fstate) == TEST_EMERGENCY_ABORT) {
+		pr_err("Fail in child worker after C/R\n");
+		goto out;
+	}
+
+	if (sh->code != CLD_STOPPED || sh->status != STOP_SIGNO) {
+		fail = 1;
+		pr_err("Process is not in correct state after C/R."
+		       " Expected stop signo: %d. Get stop signo: %d\n",
+		       STOP_SIGNO, sh->status);
+	}
+
+	if (!fail)
+		pass();
+
+	futex_set_and_wake(&sh->fstate, TEST_EXIT);
+out:
+	if (pid > 0)
+		wait(NULL);
+
+	munmap(sh, sizeof(struct shared));
+
+	return fail;
+}
diff --git a/test/zdtm/static/stopped04.c b/test/zdtm/static/stopped04.c
new file mode 100644
index 000000000..237094ca4
--- /dev/null
+++ b/test/zdtm/static/stopped04.c
@@ -0,0 +1,135 @@
+#include <signal.h>
+#include <sys/wait.h>
+#include <sys/mman.h>
+
+#include "zdtmtst.h"
+#include "lock.h"
+
+const char *test_doc = "Check, that stopped by SIGTSTP tasks are restored correctly";
+const char *test_author = "Yuriy Vasiliev <yuriy.vasiliev@openvz.org>";
+
+const char *stop_sigstr = "SIGTSTP";
+enum {
+	FUTEX_INITIALIZED = 0,
+	TEST_CRIU,
+	TEST_DONE,
+	TEST_EXIT,
+	TEST_EMERGENCY_ABORT,
+};
+
+struct shared {
+	futex_t fstate;
+	int status;
+	int code;
+} * sh;
+
+static int new_pgrp(void)
+{
+	sigset_t sigset;
+	siginfo_t infop;
+	int ret = 1;
+	pid_t pid;
+
+	/*
+	 * Set the PGID to avoid creating an orphaned process group,
+	 * which is not to be affected by terminal-generated stop signals.
+	 */
+	setpgid(0, 0);
+
+	sigemptyset(&sigset);
+	sigaddset(&sigset, SIGTSTP);
+	sigprocmask(SIG_BLOCK, &sigset, NULL);
+
+	pid = test_fork();
+	if (pid < 0)
+		goto err_cr;
+
+	if (pid == 0) {
+		/* wait for TEST_EXIT or TEST_EMERGENCY_ABORT*/
+		futex_wait_while_lt(&sh->fstate, TEST_EXIT);
+		exit(0);
+	}
+
+	if (kill(pid, SIGSTOP)) {
+		pr_perror("Unable to send %s", stop_sigstr);
+		goto err_cr;
+	}
+
+	if (waitid(P_PID, pid, &infop, WNOWAIT | WSTOPPED) < 0) {
+		pr_perror("Unable to waitid %d", pid);
+		goto err_cont;
+	}
+
+	if (kill(pid, SIGTSTP)) {
+		pr_perror("Unable to send %s", stop_sigstr);
+		goto err_cr;
+	}
+
+	/* Return the control back to MAIN worker to do C/R */
+	futex_set_and_wake(&sh->fstate, TEST_CRIU);
+	futex_wait_while_lt(&sh->fstate, TEST_EXIT);
+
+	ret = 0;
+err_cont:
+	kill(pid, SIGCONT);
+err_cr:
+	if (ret)
+		futex_set_and_wake(&sh->fstate, TEST_EMERGENCY_ABORT);
+	if (pid > 0)
+		wait(NULL);
+
+	return ret;
+}
+
+int main(int argc, char **argv)
+{
+	int fail = 0;
+	pid_t pid;
+
+	test_init(argc, argv);
+
+	sh = mmap(NULL, sizeof(struct shared), PROT_WRITE | PROT_READ, MAP_SHARED | MAP_ANONYMOUS, -1, 0);
+	if (sh == MAP_FAILED) {
+		pr_perror("Failed to alloc shared region");
+		return 1;
+	}
+
+	futex_set(&sh->fstate, FUTEX_INITIALIZED);
+
+	pid = test_fork();
+	if (pid < 0) {
+		fail = 1;
+		goto out;
+	}
+
+	if (pid == 0)
+		exit(new_pgrp());
+
+	/* Wait until pgrp is ready to C/R */
+	futex_wait_while_lt(&sh->fstate, TEST_CRIU);
+	if (futex_get(&sh->fstate) == TEST_EMERGENCY_ABORT) {
+		pr_err("Fail in child worker before C/R\n");
+		fail = 1;
+		goto out;
+	}
+
+	test_daemon();
+	test_waitsig();
+
+	if (futex_get(&sh->fstate) == TEST_EMERGENCY_ABORT) {
+		pr_err("Fail in child worker after C/R\n");
+		goto out;
+	}
+
+	if (!fail)
+		pass();
+
+	futex_set_and_wake(&sh->fstate, TEST_EXIT);
+out:
+	if (pid > 0)
+		wait(NULL);
+
+	munmap(sh, sizeof(struct shared));
+
+	return fail;
+}