diff -u b/core/modules/system/system.module b/core/modules/system/system.module
--- b/core/modules/system/system.module
+++ b/core/modules/system/system.module
@@ -173,14 +173,6 @@
       'render element' => 'elements',
       'base hook' => 'block',
     ),
-    'block__system_local_actions_block' => [
-      'base hook' => 'block',
-      'template' => 'block--system-local-actions-block',
-    ],
-    'block__system_tabs_block' => [
-      'base hook' => 'block',
-      'template' => 'block--system-tabs-block',
-    ],
     'system_themes_page' => array(
       'variables' => array(
         'theme_groups' => array(),
@@ -791,11 +783,11 @@
       break;
 
     case 'system_local_actions_block':
-      $variables['action_links'] = $variables['content']['action_links'];
+      $variables['content'] = $variables['content']['action_links'];
       break;
 
     case 'system_tabs_block':
-      $variables['tabs'] = $variables['content']['tabs'];
+      $variables['content'] = $variables['content']['tabs'];
       break;
 
     case 'system_powered_by_block':
reverted:
--- b/core/modules/system/templates/block--system-local-actions-block.html.twig
+++ /dev/null
@@ -1,14 +0,0 @@
-{% extends "@block/block.html.twig" %}
-{#
-/**
- * @file
- * Default theme implementation for local actions.
- *
- * Available variables:
- * - action_links: Actions local to the page, such as "Add menu" on the menu
- *   administration interface.
- */
-#}
-{% block content %}
-  {{ action_links }}
-{% endblock %}
reverted:
--- b/core/modules/system/templates/block--system-tabs-block.html.twig
+++ /dev/null
@@ -1,14 +0,0 @@
-{% extends "@block/block.html.twig" %}
-{#
-/**
- * @file
- * Default theme implementation for tabs.
- *
- * Available variables:
- * - tabs: The tabs linking to any sub-pages beneath the current page (e.g., the
- *   view and edit tabs when displaying a node).
- */
-#}
-{% block content %}
-  {{ tabs }}
-{% endblock %}
diff -u b/core/themes/classy/templates/block/block--system-local-actions-block.html.twig b/core/themes/classy/templates/block/block--system-local-actions-block.html.twig
--- b/core/themes/classy/templates/block/block--system-local-actions-block.html.twig
+++ b/core/themes/classy/templates/block/block--system-local-actions-block.html.twig
@@ -11,6 +11,6 @@
 #}
 {% block content %}
-  {% if action_links %}
-    <nav class="action-links">{{ action_links }}</nav>
+  {% if content %}
+    <nav class="action-links">{{ content }}</nav>
   {% endif %}
 {% endblock %}
diff -u b/core/themes/classy/templates/block/block--system-tabs-block.html.twig b/core/themes/classy/templates/block/block--system-tabs-block.html.twig
--- b/core/themes/classy/templates/block/block--system-tabs-block.html.twig
+++ b/core/themes/classy/templates/block/block--system-tabs-block.html.twig
@@ -10,9 +10,9 @@
  */
 #}
 {% block content %}
-  {% if tabs %}
+  {% if content %}
     <nav class="tabs" role="navigation" aria-label="{{ 'Tabs'|t }}">
-      {{ tabs }}
+      {{ content }}
     </nav>
   {% endif %}
 {% endblock %}