A rail clip assembly for securing for example a crane rail to a girder, comprises a first part to be securely attached, e.g. by welding or bolting, to the planar surface of the girder adjacent the rail, and a second part to be fixed to the first part independently of attachment of the first part to the girder. The second part has a lateral surface for abutment with a lateral face of the rail and the parts have laterally directed cooperating surfaces by which forces applied by the rail to the clip assembly are transmitted via the second part to the first part of the clip assembly. The cooperating surfaces are inclined to the direction of extent of the rail and the second part has an elongate aperture for receiving the fixing means which is elongate in the same direction to permit relative adjustment movement between the parts while maintaining the cooperating surfaces in contact. At least the first part is wedge shaped and increasing in thickness in the direction of approach of the cooperating surfaces to the rail so that lateral forces applied by the rail to the clip assembly produce and are resisted by an increase in the tension in the fixing means.