diff --git a/mod/quiz/lang/en/quiz.php b/mod/quiz/lang/en/quiz.php
index 30933e8f795..2147fd5ae18 100644
--- a/mod/quiz/lang/en/quiz.php
+++ b/mod/quiz/lang/en/quiz.php
@@ -335,6 +335,7 @@ $string['graceperiod_desc'] = 'If what to do when time expires is set to \'Allow
 $string['graceperiod_help'] = 'If what to do when time expires is set to \'Allow a grace period to submit, but not change any responses\', the amount of extra time that is allowed.';
 $string['graceperiodmin'] = 'Last submission grace period';
 $string['graceperiodmin_desc'] = 'There is a potential problem right at the end of the quiz. On the one hand, we want to let students continue working right up until the last second - with the help of the timer that automatically submits the quiz when time runs out. On the other hand, the server may then be overloaded, and take some time to get to process the responses. Therefore, we will accept responses for up to this many seconds after time expires, so they are not penalised for the server being slow. However, the student could cheat and get this many seconds to answer the quiz. You have to make a trade-off based on how much you trust the performance of your server during quizzes.';
+$string['graceperiodtoosmall'] = 'The grace period must be at more than {$a}.';
 $string['grade'] = 'Grade';
 $string['gradeall'] = 'Grade all';
 $string['gradeaverage'] = 'Average grade';
diff --git a/mod/quiz/mod_form.php b/mod/quiz/mod_form.php
index 94336a65852..0b101ece09d 100644
--- a/mod/quiz/mod_form.php
+++ b/mod/quiz/mod_form.php
@@ -502,6 +502,14 @@ class mod_quiz_mod_form extends moodleform_mod {
             $errors['timeclose'] = get_string('closebeforeopen', 'quiz');
         }
 
+        // Check that the grace period is not too short.
+        if ($data['overduehandling'] == 'graceperiod') {
+            $graceperiodmin = get_config('quiz', 'graceperiodmin');
+            if ($data['graceperiod'] <= $graceperiodmin) {
+                $errors['graceperiod'] = get_string('graceperiodtoosmall', 'quiz', format_time($graceperiodmin));
+            }
+        }
+
         // Check the boundary value is a number or a percentage, and in range.
         $i = 0;
         while (!empty($data['feedbackboundaries'][$i] )) {
diff --git a/mod/quiz/processattempt.php b/mod/quiz/processattempt.php
index 6d1fc60c4b9..f355eb90ad4 100644
--- a/mod/quiz/processattempt.php
+++ b/mod/quiz/processattempt.php
@@ -65,12 +65,14 @@ if ($page == -1) {
 
 // If there is only a very small amount of time left, there is no point trying
 // to show the student another page of the quiz. Just finish now.
+$graceperiodmin = null;
 $accessmanager = $attemptobj->get_access_manager($timenow);
 $timeleft = $accessmanager->get_time_left($attemptobj->get_attempt(), $timenow);
 $toolate = false;
 if ($timeleft !== false && $timeleft < QUIZ_MIN_TIME_TO_CONTINUE) {
     $timeup = true;
-    if ($timeleft < -get_config('quiz', 'graceperiodmin')) {
+    $graceperiodmin = get_config('quiz', 'graceperiodmin');
+    if ($timeleft < -$graceperiodmin) {
         $toolate = true;
     }
 }
@@ -97,9 +99,19 @@ if ($attemptobj->is_finished()) {
 
 // If time is running out, trigger the appropriate action.
 $becomingoverdue = false;
+$becomingabandoned = false;
 if ($timeup) {
-    if ($attemptobj->get_quiz()->overduehandling == 'graceperiod') {
-        $becomingoverdue = true;
+    if ($attemptobj->get_quiz()->overduehandling == 'graceperiod') {#
+        if (is_null($graceperiodmin)) {
+            $graceperiodmin = get_config('quiz', 'graceperiodmin');
+        }
+        if ($timeleft < -$attemptobj->get_quiz()->graceperiod - $graceperiodmin) {
+            // Grace period has run out.
+            $finishattempt = true;
+            $becomingabandoned = true;
+        } else {
+            $becomingoverdue = true;
+        }
     } else {
         $finishattempt = true;
     }
@@ -150,7 +162,11 @@ add_to_log($attemptobj->get_courseid(), 'quiz', 'close attempt',
 
 // Update the quiz attempt record.
 try {
-    $attemptobj->process_finish($timenow, !$toolate);
+    if ($becomingabandoned) {
+        $attemptobj->process_abandon($timenow, true);
+    } else {
+        $attemptobj->process_finish($timenow, !$toolate);
+    }
 
 } catch (question_out_of_sequence_exception $e) {
     print_error('submissionoutofsequencefriendlymessage', 'question',
diff --git a/mod/quiz/summary.php b/mod/quiz/summary.php
index 0b1cdb0e762..303638f013c 100644
--- a/mod/quiz/summary.php
+++ b/mod/quiz/summary.php
@@ -46,11 +46,6 @@ if (!$attemptobj->is_preview_user()) {
     $attemptobj->require_capability('mod/quiz:attempt');
 }
 
-// If the attempt is already closed, redirect them to the review page.
-if ($attemptobj->is_finished()) {
-    redirect($attemptobj->review_url());
-}
-
 if ($attemptobj->is_preview_user()) {
     navigation_node::override_active_url($attemptobj->start_attempt_url());
 }
@@ -69,6 +64,14 @@ if ($accessmanager->is_preflight_check_required($attemptobj->get_attemptid())) {
 
 $displayoptions = $attemptobj->get_display_options(false);
 
+// If the attempt is now overdue, or abandoned, deal with that.
+$attemptobj->handle_if_time_expired(time(), true);
+
+// If the attempt is already closed, redirect them to the review page.
+if ($attemptobj->is_finished()) {
+    redirect($attemptobj->review_url());
+}
+
 // Log this page view.
 add_to_log($attemptobj->get_courseid(), 'quiz', 'view summary',
         'summary.php?attempt=' . $attemptobj->get_attemptid(),