diff -u b/composer.json b/composer.json
--- b/composer.json
+++ b/composer.json
@@ -49,12 +49,10 @@
     },
     "scripts": {
         "pre-autoload-dump": "Drupal\\Core\\Composer\\Composer::preAutoloadDump",
-        "post-autoload-dump": [
-          "Drupal\\Core\\Composer\\Composer::ensureHtaccess",
-          "Drupal\\Core\\Composer\\Composer::upgradePHPUnit"
-        ],
+        "post-autoload-dump": "Drupal\\Core\\Composer\\Composer::ensureHtaccess",
         "post-package-install": "Drupal\\Core\\Composer\\Composer::vendorTestCodeCleanup",
         "post-package-update": "Drupal\\Core\\Composer\\Composer::vendorTestCodeCleanup",
+        "post-install-cmd": "Drupal\\Core\\Composer\\Composer::upgradePHPUnit",
         "drupal-phpunit-upgrade": "@composer upgrade phpunit/phpunit --with-dependencies --no-progress",
         "phpcs": "phpcs --standard=core/phpcs.xml.dist --runtime-set installed_paths $($COMPOSER_BINARY config vendor-dir)/drupal/coder/coder_sniffer --",
         "phpcbf": "phpcbf --standard=core/phpcs.xml.dist --runtime-set installed_paths $($COMPOSER_BINARY config vendor-dir)/drupal/coder/coder_sniffer --"
diff -u b/core/lib/Drupal/Core/Composer/Composer.php b/core/lib/Drupal/Core/Composer/Composer.php
--- b/core/lib/Drupal/Core/Composer/Composer.php
+++ b/core/lib/Drupal/Core/Composer/Composer.php
@@ -6,7 +6,6 @@
 use Composer\Script\Event;
 use Composer\Installer\PackageEvent;
 use Composer\Semver\Constraint\Constraint;
-use PHPUnit\Runner\Version;
 
 /**
  * Provides static functions for composer script events.
@@ -150,15 +149,23 @@
    * @param \Composer\Script\Event $event
    */
   public static function upgradePHPUnit(Event $event) {
-    if (class_exists('PHPUnit_Runner_Version')) {
-      $phpunit_version = \PHPUnit_Runner_Version::id();
+    $repository = $event->getComposer()->getRepositoryManager()->getLocalRepository();
+    // This is, essentially, a null constraint. We only care whether the package
+    // is present in the vendor directory yet, but findPackage() requires it.
+    $constraint = new Constraint('>', '');
+    $phpunit_package = $repository->findPackage('phpunit/phpunit', $constraint);
+    if (!$phpunit_package) {
+      // There is nothing to do. The user is probably installing using the
+      // --no-dev flag.
+      return;
     }
-    if (class_exists('\PHPUnit\Runner\Version')) {
-      $phpunit_version = Version::id();
-    }
-    // @todo if we haven't determine version throw an error.
-    if (version_compare(PHP_MAJOR_VERSION . '.' . PHP_MINOR_VERSION, '7.1') >= 0 && version_compare($phpunit_version, '6.0') < 0) {
-      $event->getComposer()->getEventDispatcher()->dispatchScript('drupal-phpunit-upgrade');
+
+    // If the PHP version is 7.1 or above and PHPUnit is less than version 6
+    // call the drupal-phpunit-upgrade script to upgrade PHPUnit.
+    if (version_compare(PHP_MAJOR_VERSION . '.' . PHP_MINOR_VERSION, '7.1') >= 0 && version_compare($phpunit_package->getVersion(), '6.0') < 0) {
+      $event->getComposer()
+        ->getEventDispatcher()
+        ->dispatchScript('drupal-phpunit-upgrade');
     }
   }
 
diff -u b/core/tests/Drupal/Tests/Component/DependencyInjection/ContainerTest.php b/core/tests/Drupal/Tests/Component/DependencyInjection/ContainerTest.php
--- b/core/tests/Drupal/Tests/Component/DependencyInjection/ContainerTest.php
+++ b/core/tests/Drupal/Tests/Component/DependencyInjection/ContainerTest.php
@@ -987,8 +987,11 @@
    * Compatibility layer for PHPUnit 6 to support PHPUnit 4 code.
    *
    * @param mixed $class
+   *   The expected exception class.
    * @param string $message
+   *   The expected exception message.
    * @param int $exception_code
+   *   The expected exception code.
    */
   public function setExpectedException($class, $message = '', $exception_code = NULL) {
     if (method_exists($this, 'expectException')) {
diff -u b/core/tests/Drupal/Tests/Component/Plugin/DefaultFactoryTest.php b/core/tests/Drupal/Tests/Component/Plugin/DefaultFactoryTest.php
--- b/core/tests/Drupal/Tests/Component/Plugin/DefaultFactoryTest.php
+++ b/core/tests/Drupal/Tests/Component/Plugin/DefaultFactoryTest.php
@@ -148,8 +148,11 @@
    * Compatibility layer for PHPUnit 6 to support PHPUnit 4 code.
    *
    * @param mixed $class
+   *   The expected exception class.
    * @param string $message
+   *   The expected exception message.
    * @param int $exception_code
+   *   The expected exception code.
    */
   public function setExpectedException($class, $message = '', $exception_code = NULL) {
     if (method_exists($this, 'expectException')) {
only in patch2:
unchanged:
--- a/core/tests/Drupal/Tests/PhpunitCompatibilityTrait.php
+++ b/core/tests/Drupal/Tests/PhpunitCompatibilityTrait.php
@@ -116,6 +116,31 @@ public function createMock($originalClassName) {
     }
   }
 
+  /**
+   * Compatibility layer for PHPUnit 6 to support PHPUnit 4 code.
+   *
+   * @param mixed $class
+   *   The expected exception class.
+   * @param string $message
+   *   The expected exception message.
+   * @param int $exception_code
+   *   The expected exception code.
+   */
+  public function setExpectedException($class, $message = '', $exception_code = NULL) {
+    if (method_exists($this, 'expectException')) {
+      $this->expectException($class);
+      if (!empty($message)) {
+        $this->expectExceptionMessage($message);
+      }
+      if ($exception_code !== NULL) {
+        $this->expectExceptionCode($exception_code);
+      }
+    }
+    else {
+      parent::setExpectedException($class, $message, $exception_code);
+    }
+  }
+
   /**
    * Checks if the trait is used in a class that has a method.
    *