An attachment system for a snow chain is disclosed, comprising a rolling track (1, 2a, 2b, 12) joined to a plurality of connecting arms (3) converging towards a common central structure (4), wherein a plurality of elastic ropes (5) forming elastic attachments between said plurality of connecting arms (3) and an anchoring ring (7) fixed to a rim (C) of a wheel, and wherein at least an inextensible linear element (9) is further provided, which may be engaged with or disengaged from a working position in which it is apt to replace the elastic attachment of at least one of said elastic ropes (5) with an inextensible attachment.