The invention relates to a rail fastening system on a sleeper, comprising fastening screws and loop-type tension clips (2, 200), wherein the gauge can be horizontally adjusted in a continuous fashion by means of wedge elements (24, 224). The rails (S, S1) are arranged on a ribbed plate (1, 100) the ribs (16, 17, 116, 117) of which extend at an angle to the rail and a wedge (24, 224) is interposed between the rail base (SF) and the ribs (16, 17, 116, 117) and is mobile in the longitudinal direction of the rail. The wedge is preferably guided on the bearing (1, 100).