A resilient rail fixing device for track installations with good torsional resistance and positive lateral hold for the rail has a design whih ensures the straightforward production of the clamp clips (3) and the secure co-operation of the clamp clips (3) with the anchoring parts (1,2). The clamp clip (3) is produced as a flexible moulding of cold-bendable steel and has four resilient rod sections (31', 34' and 31", 34") as abutment legs (3' and 3"). Each bracing part (26', 26") of the clamp clip (3) is shaped integrally onto two independent resilient rod secions (31' and 34' or 31' and 34") which have been stressed to torsion. Two inner resilient rod sections (31' and 31") are produced integrally with a transverse connecting piece (33), while the two outer resilient rod sections (34' and 34") are supportd by U-Shaped deflections (35' and 35") on the top of the transverse connecting piece (33).