$dbRes=mysql_connect($DB_HOST,$DB_USER,$DB_PASS) 
   OR die("Der Server ($DB_HOST) konnte "
          ."nicht konnektiert werden.");
mysql_select_db($DB_NAME)
   OR die("Die Datenbank ($DB_NAME) konnte "
          ."nicht ausgewählt werden.");

$dbRes = new mysqli($DB_HOST, $DB_USER, $DB_PASS, $DB_NAME);
if ($dbRes->connect_error) {
   die('Connect Error ('
       .$dbRes->connect_errno.') '
       .$dbRes->connect_error);
};

$quRes = mysql_query("sql statement");

$quRes = $dbRes->query("sql statement");

$ergRow = mysql_fetch_assoc($quRes);

$ergObj = mysql_fetch_object($quRes);

$ergRow = mysql_fetch_array($quRes,MYSQL_ASSOC);

$ergRow = $quRes->fetch_assoc();

$ergObj = $quRes->fetch_object();

$ergRow = $quRes->fetch_array(MYSQLI_ASSOC);

$rows = mysql_num_rows($quRes);

$rows = $quRes->num_rows;

ist ein Attribut, keine Methode