diff --git a/tests/compat-in-docker.sh b/tests/compat-in-docker.sh
index aef0a07289..3a1cd2144c 100755
--- a/tests/compat-in-docker.sh
+++ b/tests/compat-in-docker.sh
@@ -42,13 +42,13 @@ esac
 
 case "${GNUTLS_CLI:-default}" in
     "legacy")  export GNUTLS_CLI="/usr/local/gnutls-3.3.8/bin/gnutls-cli";;
-    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.6.5/bin/gnutls-cli";;
+    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.7.2/bin/gnutls-cli";;
     *) ;;
 esac
 
 case "${GNUTLS_SERV:-default}" in
     "legacy")  export GNUTLS_SERV="/usr/local/gnutls-3.3.8/bin/gnutls-serv";;
-    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.6.5/bin/gnutls-serv";;
+    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.7.2/bin/gnutls-serv";;
     *) ;;
 esac
 
diff --git a/tests/docker/bionic/Dockerfile b/tests/docker/bionic/Dockerfile
index 1d24aa3268..41789c677c 100644
--- a/tests/docker/bionic/Dockerfile
+++ b/tests/docker/bionic/Dockerfile
@@ -137,29 +137,29 @@ RUN cd /tmp \
 ENV GNUTLS_CLI=/usr/local/gnutls-3.4.10/bin/gnutls-cli
 ENV GNUTLS_SERV=/usr/local/gnutls-3.4.10/bin/gnutls-serv
 
-# Build libnettle 3.4 (needed by gnutls next)
+# Build libnettle 3.7.3 (needed by gnutls next)
 RUN cd /tmp \
-    && wget https://ftp.gnu.org/gnu/nettle/nettle-3.4.1.tar.gz -qO- | tar xz \
-    && cd nettle-3.4.1 \
+    && wget https://ftp.gnu.org/gnu/nettle/nettle-3.7.3.tar.gz -qO- | tar xz \
+    && cd nettle-3.7.3 \
     && ./configure --disable-documentation \
     && make ${MAKEFLAGS_PARALLEL} \
     && make install \
     && /sbin/ldconfig \
     && rm -rf /tmp/nettle*
 
-# Build gnutls next (3.6.5)
+# Build gnutls next (3.7.2)
 RUN cd /tmp \
-    && wget https://www.gnupg.org/ftp/gcrypt/gnutls/v3.6/gnutls-3.6.5.tar.xz -qO- | tar xJ \
-    && cd gnutls-3.6.5 \
-    && ./configure --prefix=/usr/local/gnutls-3.6.5 --exec_prefix=/usr/local/gnutls-3.6.5 \
+    && wget https://www.gnupg.org/ftp/gcrypt/gnutls/v3.7/gnutls-3.7.2.tar.xz -qO- | tar xJ \
+    && cd gnutls-3.7.2 \
+    && ./configure --prefix=/usr/local/gnutls-3.7.2 --exec_prefix=/usr/local/gnutls-3.7.2 \
         --with-included-libtasn1 --with-included-unistring --without-p11-kit \
         --disable-shared --disable-guile --disable-doc \
     && make ${MAKEFLAGS_PARALLEL} \
     && make install \
     && rm -rf /tmp/gnutls*
 
-ENV GNUTLS_NEXT_CLI=/usr/local/gnutls-3.6.5/bin/gnutls-cli
-ENV GNUTLS_NEXT_SERV=/usr/local/gnutls-3.6.5/bin/gnutls-serv
+ENV GNUTLS_NEXT_CLI=/usr/local/gnutls-3.7.2/bin/gnutls-cli
+ENV GNUTLS_NEXT_SERV=/usr/local/gnutls-3.7.2/bin/gnutls-serv
 
 RUN pip3 install --no-cache-dir \
     mbed-host-tests \
diff --git a/tests/ssl-opt-in-docker.sh b/tests/ssl-opt-in-docker.sh
index 401a69c569..e7bb01d8ca 100755
--- a/tests/ssl-opt-in-docker.sh
+++ b/tests/ssl-opt-in-docker.sh
@@ -42,13 +42,13 @@ esac
 
 case "${GNUTLS_CLI:-default}" in
     "legacy")  export GNUTLS_CLI="/usr/local/gnutls-3.3.8/bin/gnutls-cli";;
-    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.6.5/bin/gnutls-cli";;
+    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.7.2/bin/gnutls-cli";;
     *) ;;
 esac
 
 case "${GNUTLS_SERV:-default}" in
     "legacy")  export GNUTLS_SERV="/usr/local/gnutls-3.3.8/bin/gnutls-serv";;
-    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.6.5/bin/gnutls-serv";;
+    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.7.2/bin/gnutls-serv";;
     *) ;;
 esac
 
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index ad925f0f0c..3e199e2881 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -405,6 +405,44 @@ requires_gnutls_tls1_3() {
     fi
 }
 
+# Check %NO_TICKETS option
+requires_gnutls_next_no_ticket() {
+    requires_gnutls_next
+    if [ "$GNUTLS_NEXT_AVAILABLE" = "NO" ]; then
+        GNUTLS_NO_TICKETS_AVAILABLE="NO"
+    fi
+    if [ -z "${GNUTLS_NO_TICKETS_AVAILABLE:-}" ]; then
+        if $GNUTLS_NEXT_CLI --priority-list 2>&1 | grep NO_TICKETS >/dev/null
+        then
+            GNUTLS_NO_TICKETS_AVAILABLE="YES"
+        else
+            GNUTLS_NO_TICKETS_AVAILABLE="NO"
+        fi
+    fi
+    if [ "$GNUTLS_NO_TICKETS_AVAILABLE" = "NO" ]; then
+        SKIP_NEXT="YES"
+    fi
+}
+
+# Check %DISABLE_TLS13_COMPAT_MODE option
+requires_gnutls_next_disable_tls13_compat() {
+    requires_gnutls_next
+    if [ "$GNUTLS_NEXT_AVAILABLE" = "NO" ]; then
+        GNUTLS_DISABLE_TLS13_COMPAT_MODE_AVAILABLE="NO"
+    fi
+    if [ -z "${GNUTLS_DISABLE_TLS13_COMPAT_MODE_AVAILABLE:-}" ]; then
+        if $GNUTLS_NEXT_CLI --priority-list 2>&1 | grep DISABLE_TLS13_COMPAT_MODE >/dev/null
+        then
+            GNUTLS_DISABLE_TLS13_COMPAT_MODE_AVAILABLE="YES"
+        else
+            GNUTLS_DISABLE_TLS13_COMPAT_MODE_AVAILABLE="NO"
+        fi
+    fi
+    if [ "$GNUTLS_DISABLE_TLS13_COMPAT_MODE_AVAILABLE" = "NO" ]; then
+        SKIP_NEXT="YES"
+    fi
+}
+
 # skip next test if IPv6 isn't available on this host
 requires_ipv6() {
     if [ -z "${HAS_IPV6:-}" ]; then
@@ -8589,11 +8627,13 @@ run_test    "TLS1.3: Test openssl tls1_3 feature" \
             -c "TLS 1.3" \
             -s "TLS 1.3"
 
-# gnutls feature tests: check if tls1.3 exists.
+# gnutls feature tests: check if TLS 1.3 is supported as well as the NO_TICKETS and DISABLE_TLS13_COMPAT_MODE options.
 requires_gnutls_tls1_3
+requires_gnutls_next_no_ticket
+requires_gnutls_next_disable_tls13_compat
 run_test    "TLS1.3: Test gnutls tls1_3 feature" \
-            "$G_NEXT_SRV --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3" \
-            "$G_NEXT_CLI localhost --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3 -V" \
+            "$G_NEXT_SRV --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:%NO_TICKETS:%DISABLE_TLS13_COMPAT_MODE" \
+            "$G_NEXT_CLI localhost --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:%NO_TICKETS:%DISABLE_TLS13_COMPAT_MODE -V" \
             0 \
             -s "Version: TLS1.3" \
             -c "Version: TLS1.3"