diff -u b/core/modules/system/tests/modules/ajax_test/js/insert-ajax.js b/core/modules/system/tests/modules/ajax_test/js/insert-ajax.js
--- b/core/modules/system/tests/modules/ajax_test/js/insert-ajax.js
+++ b/core/modules/system/tests/modules/ajax_test/js/insert-ajax.js
@@ -20,6 +20,8 @@
         var myAjaxObject = Drupal.ajax(ajaxSettings);
         myAjaxObject.execute();
       });
+
+      $(context).addClass('processed');
     }
   };
 })(jQuery, window, Drupal, drupalSettings);
diff -u b/core/tests/Drupal/FunctionalJavascriptTests/Ajax/AjaxTest.php b/core/tests/Drupal/FunctionalJavascriptTests/Ajax/AjaxTest.php
--- b/core/tests/Drupal/FunctionalJavascriptTests/Ajax/AjaxTest.php
+++ b/core/tests/Drupal/FunctionalJavascriptTests/Ajax/AjaxTest.php
@@ -83,33 +83,41 @@
   }
 
   /**
-   * Tests that various AJAX responses are correctly wrapped.
+   * Tests that various AJAX responses with DOM elements are correctly inserted.
+   *
+   * After inserting DOM elements, Drupal JavaScript behaviors should be
+   * reattached and all 'root' elements of type Node.ELEMENT_NODE need to be
+   * part of the context.
    */
-  public function testWrap() {
+  public function testInsert() {
     $assert = $this->assertSession();
     $this->drupalGet('ajax-test/insert');
 
     // Test that no additional wrapper is added when inserting already wrapped
-    // response data.
+    // response data and all root node elements (context) are processed
+    // correctly.
     $this->clickLink('Link pre-wrapped');
     $assert->assertWaitOnAjaxRequest();
-    $assert->responseContains('<div class="pre-wrapped">pre-wrapped</div>');
+    $assert->responseContains('<div class="pre-wrapped processed">pre-wrapped</div>');
 
     // Test that no additional empty leading div is added when the return
-    // value had a leading space.
+    // value had a leading space and all root node elements (context) are
+    // processed correctly.
     $this->clickLink('Link pre-wrapped-leading-whitespace');
     $assert->assertWaitOnAjaxRequest();
-    $assert->responseContains('<div id="ajax-target"><div class="pre-wrapped-leading-whitespace">pre-wrapped-leading-whitespace</div></div>');
+    $assert->responseContains('<div id="ajax-target"><div class="pre-wrapped-leading-whitespace processed">pre-wrapped-leading-whitespace</div></div>');
 
-    // Test that unwrapped response data (text node) is inserted wrapped.
+    // Test that unwrapped response data (text node) is inserted wrapped and all
+    // root node elements (context) are processed correctly.
     $this->clickLink('Link not-wrapped');
     $assert->assertWaitOnAjaxRequest();
-    $assert->responseContains('<div>not-wrapped</div>');
+    $assert->responseContains('<div class="processed">not-wrapped</div>');
 
-    // Test that wrappend and unwrapped response data is inserted correctly.
+    // Test that wrappend and unwrapped response data is inserted correctly and
+    // all root node elements (context) are processed correctly.
     $this->clickLink('Link mixed');
     $assert->assertWaitOnAjaxRequest();
-    $assert->responseContains('<div> foo <!-- COMMENT -->  foo bar</div><div class="a class"><p>some string</p></div><div> additional wrapped strings, <!-- ANOTHER COMMENT --> </div><p>final string</p>');
+    $assert->responseContains('<div class="processed"> foo <!-- COMMENT -->  foo bar</div><div class="a class processed"><p>some string</p></div><div class="processed"> additional wrapped strings, <!-- ANOTHER COMMENT --> </div><p class="processed">final string</p>');
   }
 
 }