diff --git a/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
index f7dc640..f0a590a 100644
--- a/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
+++ b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
@@ -127,7 +127,7 @@ protected function getLibraryDefinitions($extension) {
         }
       }
       else {
-        // Apply libraries extend.
+        // If libraries are not overridden, then apply libraries extend.
         $libraries[$name] = $this->applyLibrariesExtend($extension, $name, $definition);
       }
     }
@@ -153,12 +153,12 @@ protected function getLibraryDefinitions($extension) {
    * @throws \Drupal\Core\Asset\Exception\InvalidLibrariesExtendSpecificationException
    */
   protected function applyLibrariesExtend($extension, $library_name, $library_definition) {
-    $active_theme = $this->themeManager->getActiveTheme()->getLibrariesExtend();
-    if (!empty($active_theme["$extension/$library_name"])) {
-      foreach ($active_theme["$extension/$library_name"] as $library_extend_name) {
+    $libraries_extend = $this->themeManager->getActiveTheme()->getLibrariesExtend();
+    if (!empty($libraries_extend["$extension/$library_name"])) {
+      foreach ($libraries_extend["$extension/$library_name"] as $library_extend_name) {
         if (!is_string($library_extend_name)) {
           // Only string library names are allowed.
-          throw new InvalidLibrariesExtendSpecificationException('The libraries-extend specification must be a string.');
+          throw new InvalidLibrariesExtendSpecificationException('The libraries-extend specification for each library must be a list of strings.');
         }
         list($new_extension, $new_library_name) = explode('/', $library_extend_name, 2);
         $new_libraries = $this->get($new_extension);
@@ -166,7 +166,7 @@ protected function applyLibrariesExtend($extension, $library_name, $library_defi
           $library_definition = NestedArray::mergeDeep($library_definition, $new_libraries[$new_library_name]);
         }
         else {
-          throw new InvalidLibrariesExtendSpecificationException(sprintf('The specified library %s does not exist.', $library_extend_name));
+          throw new InvalidLibrariesExtendSpecificationException(sprintf('The specified library "%s" does not exist.', $library_extend_name));
         }
       }
     }
diff --git a/core/lib/Drupal/Core/Theme/ThemeInitialization.php b/core/lib/Drupal/Core/Theme/ThemeInitialization.php
index e9bae2d..e310777 100644
--- a/core/lib/Drupal/Core/Theme/ThemeInitialization.php
+++ b/core/lib/Drupal/Core/Theme/ThemeInitialization.php
@@ -189,14 +189,28 @@ public function getActiveTheme(Extension $theme, array $base_themes = []) {
     foreach ($base_themes as $base) {
       if (!empty($base->info['libraries-extend'])) {
         foreach ($base->info['libraries-extend'] as $library => $extend) {
-          $values['libraries_extend'][$library] = $extend;
+          if (isset($values['libraries_extend'][$library])) {
+            // Merge if libraries-extend has already been defined for this
+            // library.
+            $values['libraries_extend'][$library] = array_merge($values['libraries_extend'][$library], $extend);
+          }
+          else {
+            $values['libraries_extend'][$library] = $extend;
+          }
         }
       }
     }
     // Add libraries extend declared by this theme.
     if (!empty($theme->info['libraries-extend'])) {
       foreach ($theme->info['libraries-extend'] as $library => $extend) {
-        $values['libraries_extend'][$library] = $extend;
+        if (isset($values['libraries_extend'][$library])) {
+          // Merge if libraries-extend has already been defined for this
+          // library.
+          $values['libraries_extend'][$library] = array_merge($values['libraries_extend'][$library], $extend);
+        }
+        else {
+          $values['libraries_extend'][$library] = $extend;
+        }
       }
     }
 
diff --git a/core/modules/system/src/Tests/Asset/LibraryDiscoveryIntegrationTest.php b/core/modules/system/src/Tests/Asset/LibraryDiscoveryIntegrationTest.php
index a535ea8..2de5680 100644
--- a/core/modules/system/src/Tests/Asset/LibraryDiscoveryIntegrationTest.php
+++ b/core/modules/system/src/Tests/Asset/LibraryDiscoveryIntegrationTest.php
@@ -7,6 +7,7 @@
 
 namespace Drupal\system\Tests\Asset;
 
+use Drupal\Core\Asset\Exception\InvalidLibrariesExtendSpecificationException;
 use Drupal\Core\Asset\Exception\InvalidLibrariesOverrideSpecificationException;
 use Drupal\simpletest\KernelTestBase;
 
@@ -173,6 +174,37 @@ public function testLibrariesExtend() {
     $this->assertAssetInLibrary('core/modules/system/tests/themes/test_theme_libraries_extend/css/extend_1.css', 'classy', 'book-navigation', 'css');
     $this->assertAssetInLibrary('core/modules/system/tests/themes/test_theme_libraries_extend/js/extend_1.js', 'classy', 'book-navigation', 'js');
     $this->assertAssetInLibrary('core/modules/system/tests/themes/test_theme_libraries_extend/css/extend_2.css', 'classy', 'book-navigation', 'css');
+
+    // Activate a sub theme and confirm that it inherits the library assets
+    // extended in the base theme as well as its own.
+    $this->assertNoAssetInLibrary('core/modules/system/tests/themes/test_basetheme/css/base-libraries-extend.css', 'classy', 'base', 'css');
+    $this->assertNoAssetInLibrary('core/modules/system/tests/themes/test_subtheme/css/sub-libraries-extend.css', 'classy', 'base', 'css');
+    $this->activateTheme('test_subtheme');
+    $this->assertAssetInLibrary('core/modules/system/tests/themes/test_basetheme/css/base-libraries-extend.css', 'classy', 'base', 'css');
+    $this->assertAssetInLibrary('core/modules/system/tests/themes/test_subtheme/css/sub-libraries-extend.css', 'classy', 'base', 'css');
+
+    // Activate test theme that extends with a non-existent library. An
+    // exception should be thrown.
+    $this->activateTheme('test_theme_libraries_extend');
+    try {
+      $this->libraryDiscovery->getLibraryByName('core', 'drupal.dialog');
+      $this->fail('Throw Exception when specifying non-existent libraries-extend.');
+    }
+    catch (InvalidLibrariesExtendSpecificationException $e) {
+      $expected_message = 'The specified library "test_theme_libraries_extend/non_existent_library" does not exist.';
+      $this->assertEqual($e->getMessage(), $expected_message, 'Throw Exception when specifying non-existent libraries-extend.');
+    }
+
+    // Also, test non-string libraries-extend. An exception should be thrown.
+    $this->container->get('theme_installer')->install(['test_theme']);
+    try {
+      $this->libraryDiscovery->getLibraryByName('test_theme', 'collapse');
+      $this->fail('Throw Exception when specifying non-string libraries-extend.');
+    }
+    catch (InvalidLibrariesExtendSpecificationException $e) {
+      $expected_message = 'The libraries-extend specification for each library must be a list of strings.';
+      $this->assertEqual($e->getMessage(), $expected_message, 'Throw Exception when specifying non-string libraries-extend.');
+    }
   }
 
   /**
diff --git a/core/modules/system/tests/themes/test_basetheme/test_basetheme.info.yml b/core/modules/system/tests/themes/test_basetheme/test_basetheme.info.yml
index 3637a0c..7b76ded 100644
--- a/core/modules/system/tests/themes/test_basetheme/test_basetheme.info.yml
+++ b/core/modules/system/tests/themes/test_basetheme/test_basetheme.info.yml
@@ -15,3 +15,7 @@ libraries-override:
     css:
       component:
         assets/vendor/farbtastic/farbtastic.css: css/farbtastic.css
+
+libraries-extend:
+  classy/base:
+    - test_basetheme/global-styling
diff --git a/core/modules/system/tests/themes/test_basetheme/test_basetheme.libraries.yml b/core/modules/system/tests/themes/test_basetheme/test_basetheme.libraries.yml
index f7529ea..b3d3406 100644
--- a/core/modules/system/tests/themes/test_basetheme/test_basetheme.libraries.yml
+++ b/core/modules/system/tests/themes/test_basetheme/test_basetheme.libraries.yml
@@ -5,3 +5,4 @@ global-styling:
       base-add.css: {}
       base-add.sub-remove.css: {}
       samename.css: {}
+      css/base-libraries-extend.css: {}
diff --git a/core/modules/system/tests/themes/test_subtheme/test_subtheme.info.yml b/core/modules/system/tests/themes/test_subtheme/test_subtheme.info.yml
index 6883e5a..b217374 100644
--- a/core/modules/system/tests/themes/test_subtheme/test_subtheme.info.yml
+++ b/core/modules/system/tests/themes/test_subtheme/test_subtheme.info.yml
@@ -9,3 +9,7 @@ libraries:
 stylesheets-remove:
   - '@theme_test/css/sub-remove.css'
   - '@test_basetheme/base-add.sub-remove.css'
+
+libraries-extend:
+  classy/base:
+    - test_subtheme/global-styling
diff --git a/core/modules/system/tests/themes/test_subtheme/test_subtheme.libraries.yml b/core/modules/system/tests/themes/test_subtheme/test_subtheme.libraries.yml
index 931dffe..1fff390 100644
--- a/core/modules/system/tests/themes/test_subtheme/test_subtheme.libraries.yml
+++ b/core/modules/system/tests/themes/test_subtheme/test_subtheme.libraries.yml
@@ -4,3 +4,4 @@ global-styling:
     base:
       css/sub-add.css: {}
       css/samename.css: {}
+      css/sub-libraries-extend.css: {}
diff --git a/core/modules/system/tests/themes/test_theme_libraries_extend/test_theme_libraries_extend.info.yml b/core/modules/system/tests/themes/test_theme_libraries_extend/test_theme_libraries_extend.info.yml
index f312c89..597a5b0 100644
--- a/core/modules/system/tests/themes/test_theme_libraries_extend/test_theme_libraries_extend.info.yml
+++ b/core/modules/system/tests/themes/test_theme_libraries_extend/test_theme_libraries_extend.info.yml
@@ -8,3 +8,8 @@ libraries-extend:
   classy/book-navigation:
     - test_theme_libraries_extend/extend_one
     - test_theme_libraries_extend/extend_two
+  core/drupal.dialog:
+    - test_theme_libraries_extend/non_existent_library
+  test_theme/collapse:
+    - not_a_string:
+        expected: 'an exception'