A rim system including a rim, an adapter disc for mounting on a wheel hub of a vehicle, a plurality of wheel screws or a plurality of wheel nuts for fastening the rim to the adapter disc, a plurality of screws or a plurality of nuts for fastening the adapter disc to the wheel hub and a wheel hub centring ring for centring the adapter disc relative to the wheel hub. A rim centring ring is provided for centering the rim relative to the adapter disc.