Index: tests/phpunit/includes/testcase-ajax.php
===================================================================
--- tests/phpunit/includes/testcase-ajax.php	(revision 31037)
+++ tests/phpunit/includes/testcase-ajax.php	(working copy)
@@ -17,6 +17,15 @@
 abstract class WP_Ajax_UnitTestCase extends WP_UnitTestCase {
 
 	/**
+	 * Whether the admin_init action has been called.
+	 *
+	 * @since 4.2.0
+	 *
+	 * @var bool
+	 */
+	protected static $did_admin_init = false;
+
+	/**
 	 * Last AJAX response.  This is set via echo -or- wp_die.
 	 * @var type
 	 */
@@ -171,7 +180,11 @@
 		$_REQUEST        = array_merge( $_POST, $_GET );
 
 		// Call the hooks
-		do_action( 'admin_init' );
+		if ( ! self::$did_admin_init ) {
+			do_action( 'admin_init' );
+			self::$did_admin_init = true;
+		}
+
 		do_action( 'wp_ajax_' . $_REQUEST['action'], null );
 
 		// Save the output