diff --git a/enrol/locallib.php b/enrol/locallib.php
index ec46efaf4e..78e3735857 100644
--- a/enrol/locallib.php
+++ b/enrol/locallib.php
@@ -382,7 +382,7 @@ class course_enrolment_manager {
             foreach (get_all_user_name_fields() as $field) {
                 $conditions[] = 'u.'.$field;
             }
-            $conditions[] = $DB->sql_fullname('u.firstname', 'u.lastname');
+            $conditions['fullname'] = $DB->sql_fullname('u.firstname', 'u.lastname');
             if ($searchanywhere) {
                 $searchparam = '%' . $search . '%';
             } else {
@@ -390,8 +390,25 @@ class course_enrolment_manager {
             }
             $i = 0;
             foreach ($conditions as $key => $condition) {
-                $conditions[$key] = $DB->sql_like($condition, ":con{$i}00", false);
-                $params["con{$i}00"] = $searchparam;
+                if ($key === 'fullname') {
+                    $j = 0;
+                    $searchsplit = preg_split('/\s+/', $search);
+                    $conditionssplit = array();
+                    foreach ($searchsplit as $subsearch) {
+                        if ($searchanywhere) {
+                            $searchparam = '%' . $subsearch . '%';
+                        } else {
+                            $searchparam = $subsearch . '%';
+                        }
+                        $conditionssplit[] = $DB->sql_like($condition, ":con{$i}00{$j}", false);
+                        $params["con{$i}00{$j}"] = $searchparam;
+                        $j++;
+                    }
+                    $conditions[$key] = '(' . implode(' AND ', $conditionssplit) . ')';
+                } else {
+                    $conditions[$key] = $DB->sql_like($condition, ":con{$i}00", false);
+                    $params["con{$i}00"] = $searchparam;
+                }
                 $i++;
             }
             $tests[] = '(' . implode(' OR ', $conditions) . ')';