Abstract: With a rim (1) for wheels of vehicles, comprising a rim base serving for the reception of a support (7) of a tyre (5), said rim base is formed in one piece from a rim bottom (2) and rim flanges (3) limiting said rim bottom in a lateral manner, with the rim base consisting of a fibre composite material. In order to be able to easily manufacture a rim of this type, said rim withstanding also high strains, a preferably one-piece counter support (8) formed by a core (13) is embedded in the rim base, which counter support receives the support (7) of the tyre (5) and is rigidly connected to the rim base, wherein the counter support (8) is processed in a mechanical, especially machining, manner on the surfaces which come into contact with the support (7) of the tyre (5).