reverted:
--- b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.js
+++ /dev/null
@@ -1,22 +0,0 @@
-/**
- * @file
- *  Testing behavior for JSWebAssertTest.
- */
-
-(function ($, Drupal, drupalSettings) {
-
-  'use strict';
-
-  /**
-   * @type {Drupal~behavior}
-   *
-   * @prop {Drupal~behaviorAttach} attach
-   *   Makes changes in the DOM to be able to test the completion of AJAX in assertWaitOnAjaxRequest.
-   */
-  Drupal.behaviors.js_webassert_test = {
-    attach: function (context) {
-      $('input[name="test_assert_wait_on_ajax_input"]').val('js_webassert_test');
-    }
-  };
-
-})(jQuery, Drupal, drupalSettings);
diff -u b/core/modules/system/tests/modules/js_webassert_test/js_webassert_test.libraries.yml b/core/modules/system/tests/modules/js_webassert_test/js_webassert_test.libraries.yml
--- b/core/modules/system/tests/modules/js_webassert_test/js_webassert_test.libraries.yml
+++ b/core/modules/system/tests/modules/js_webassert_test/js_webassert_test.libraries.yml
@@ -1,7 +1,14 @@
-js_webassert_test:
+wait_for_ajax_request:
   version: VERSION
   js:
-    js/js_webassert_test.js: {}
+    js/js_webassert_test.wait_for_ajax_request.js: {}
+  dependencies:
+    - core/jquery
+    - core/drupal
+wait_for_element:
+  version: VERSION
+  js:
+    js/js_webassert_test.wait_for_element.js: {}
   dependencies:
     - core/jquery
     - core/drupal
diff -u b/core/modules/system/tests/modules/js_webassert_test/src/Form/JsWebAssertTestForm.php b/core/modules/system/tests/modules/js_webassert_test/src/Form/JsWebAssertTestForm.php
--- b/core/modules/system/tests/modules/js_webassert_test/src/Form/JsWebAssertTestForm.php
+++ b/core/modules/system/tests/modules/js_webassert_test/src/Form/JsWebAssertTestForm.php
@@ -83,6 +83,21 @@
     ];
 
     // Button to test the assertWaitOnAjaxRequest() assertion.
+    $form['test_wait_for_element_visible'] = [
+      '#type' => 'submit',
+      '#value' => $this->t('Test waitForElementVisible'),
+      '#button_type' => 'primary',
+      '#ajax' => [
+        'callback' => 'Drupal\js_webassert_test\Form\JsWebAssertTestForm::addWaitForElementVisible',
+        'progress' => [
+          'type' => 'throbber',
+          'message' => NULL,
+        ],
+        'wrapper' => 'js_webassert_test_form_wrapper',
+      ],
+    ];
+
+    // Button to test the assertWaitOnAjaxRequest() assertion.
     $form['test_assert_wait_on_ajax_request'] = [
       '#type' => 'submit',
       '#value' => $this->t('Test assertWaitOnAjaxRequest'),
@@ -151,9 +166,8 @@
    * Ajax callback for the "Test waitForAjax" button.
    */
   public static function addAssertWaitOnAjaxRequest(array $form, FormStateInterface $form_state) {
-    // Attach the library necessary for using the OpenModalDialogCommand and
-    // set the attachments for this Ajax response.
-    $form['#attached']['library'][] = 'js_webassert_test/js_webassert_test';
+    // Attach the library necessary for this test.
+    $form['#attached']['library'][] = 'js_webassert_test/wait_for_ajax_request';
 
     $form['test_assert_wait_on_ajax_input'] = [
       '#type' => 'textfield',
@@ -163,6 +177,26 @@
     return $form;
   }
 
+
+  /**
+   * Ajax callback for the "Test waitForElementVisible" button.
+   */
+  public static function addWaitForElementVisible(array $form, FormStateInterface $form_state) {
+    // Attach the library necessary for this test.
+    $form['#attached']['library'][] = 'js_webassert_test/wait_for_element';
+
+    $form['element_invisible'] = [
+      '#id' => 'js_webassert_test_element_invisible',
+      '#type' => 'submit',
+      '#value' => 'Added WaitForElementVisible',
+      '#button_type' => 'primary',
+      '#attributes' => [
+        'style' => ['display: none;'],
+      ],
+    ];
+    return $form;
+  }
+
   /**
    * {@inheritdoc}
    */
diff -u b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
--- b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
+++ b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
@@ -110,6 +110,11 @@
     // Wait for the element to be in the DOM.
     $element = $this->waitForElement($selector, $locator, $timeout);
 
+    // Element not found in the DOM, return immediately.
+    if (empty($element)) {
+      return NULL;
+    }
+
     $end = $start + $timeout / 1000.0;
     do {
       $result = $element->isVisible();
diff -u b/core/tests/Drupal/FunctionalJavascriptTests/Tests/JSWebAssertTest.php b/core/tests/Drupal/FunctionalJavascriptTests/Tests/JSWebAssertTest.php
--- b/core/tests/Drupal/FunctionalJavascriptTests/Tests/JSWebAssertTest.php
+++ b/core/tests/Drupal/FunctionalJavascriptTests/Tests/JSWebAssertTest.php
@@ -33,6 +33,7 @@
     $test_field = $page->findButton('Add field');
     $test_id = $page->findButton('Add ID');
     $test_wait_on_ajax = $page->findButton('Test assertWaitOnAjaxRequest');
+    $test_wait_on_element_visible = $page->findButton('Test waitForElementVisible');
 
     // Test the wait...() methods by first checking the fields aren't available
     // and then are available after the wait method.
@@ -69,6 +70,13 @@
     $result = $page->findField('test_assert_wait_on_ajax_input');
     $this->assertNotEmpty($result);
     $this->assertEquals('js_webassert_test', $result->getValue());
+
+    $test_wait_on_element_visible->click();
+    $result = $page->findButton('Added WaitForElementVisible');
+    $this->assertEmpty($result);
+    $result = $assert_session->waitForElementVisible('named', array('button', 'Added WaitForElementVisible'));
+    $this->assertNotEmpty($result);
+    $this->assertEquals(TRUE, $result->isVisible());
   }
 
 }
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.wait_for_ajax_request.js
@@ -0,0 +1,22 @@
+/**
+ * @file
+ *  Testing behavior for JSWebAssertTest.
+ */
+
+(function ($, Drupal, drupalSettings) {
+
+  'use strict';
+
+  /**
+   * @type {Drupal~behavior}
+   *
+   * @prop {Drupal~behaviorAttach} attach
+   *   Makes changes in the DOM to be able to test the completion of AJAX in assertWaitOnAjaxRequest.
+   */
+  Drupal.behaviors.js_webassert_test_wait_for_ajax_request = {
+    attach: function (context) {
+      $('input[name="test_assert_wait_on_ajax_input"]').val('js_webassert_test');
+    }
+  };
+
+})(jQuery, Drupal, drupalSettings);
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.wait_for_element.js
@@ -0,0 +1,22 @@
+/**
+ * @file
+ *  Testing behavior for JSWebAssertTest.
+ */
+
+(function ($, Drupal, drupalSettings) {
+
+  'use strict';
+
+  /**
+   * @type {Drupal~behavior}
+   *
+   * @prop {Drupal~behaviorAttach} attach
+   *   Makes changes in the DOM to be able to test the completion of AJAX in assertWaitOnAjaxRequest.
+   */
+  Drupal.behaviors.js_webassert_test_wait_for_element = {
+    attach: function (context) {
+      $('#js_webassert_test_element_invisible').show();
+    }
+  };
+
+})(jQuery, Drupal, drupalSettings);
only in patch2:
unchanged:
--- /dev/null
+++ b/core/tests/Drupal/FunctionalJavascriptTests/js/JSWebAssert.assertWaitOnAjaxRequest.js
@@ -0,0 +1,12 @@
+(function() {
+  function IsNotAjaxing(instance, index, array) {
+    "use strict";
+    return instance ? !instance.ajaxing : true;
+  }
+  return (
+    // Assert no AJAX request is running (via jQuery or Drupal) and no
+    // animation is running.
+    (typeof jQuery === "undefined" || (jQuery.active === 0 && jQuery(':animated').length === 0)) &&
+    (typeof Drupal === 'undefined' || typeof Drupal.ajax === 'undefined' || Drupal.ajax.instances.every(IsNotAjaxing))
+  );
+}());
\ No newline at end of file