Tandem anti-friction bearing comprising: - an inner bearing ring and an outer bearing ring, each of the said bearing rings (20, 30) delimiting at least two raceways (22, 24, 32, 34), - a first rolling body subunit with a first plurality of rolling bodies and a first cage which is arranged in a first pair of raceways (24, 34) in the inner and outer bearing rings (20, 30), - the first cage having a first ring with a plurality of axially extending projections, each projection having an axial free end, and holding pockets for the rolling bodies being provided in each case between adjacent pairs of projections, - each of the projections having a pair of radially outer lugs which extend in a circumferential direction into adjacent holding pockets, the radially outer lugs, lugs, which extend from adjacent projections into each of the holding pockets delimiting a radially outer holding surface (166, 168) for in each case one of the rolling bodies of the first plurality of rolling bodies in the corresponding holding pocket, a partially spherical surface on an inner surface of the first ring and respective radially inner, partially cylindrical surfaces which are arranged between the projections of the respective holding pocket making contact with a corresponding rolling body of the first plurality of rolling bodies; and - a second rolling body subunit with a second plurality of rolling bodies and a second cage which is arranged in a second pair of raceways (22, 32) in the inner and the outer bearing ring (20, 30), - the second cage having a second ring with a plurality of axially extending projections, each projection having an axial free end, and holding pockets for the rolling bodies being provided in each case between adjacent pairs of projections, - each of the projections having a pair of radially inner lugs which extend in the circumferential direction into adjacent holding pockets, the radially inner lugs which extend from adjacent projections into each of the holding pockets delimiting a radially inner holding surface (176, 178) for in each case one of the rolling bodies of the second plurality of rolling bodies in the corresponding holding pocket, a partially spherical surface on an inner surface of the second ring and respective radially outer, partially cylindrical surfaces which are arranged between the projections of the respective holding pocket making contact with a corresponding rolling body of the second plurality of rolling bodies; and - the free ends (61, 71) of the projections (64, 74) of the first and the second cage (60, 70) facing one another. - an inner bearing ring and an outer bearing ring, each of the said bearing rings (20, 30) delimiting at least two raceways (22, 24, 32, 34), - a first rolling body subunit with a first plurality of rolling bodies and a first cage which is arranged in a first pair of raceways (24, 34) in the inner and outer bearing rings (20, 30), - the first cage having a first ring with a plurality of axially extending projections, each projection having an axial free end, and holding pockets for the rolling bodies being provided in each case between adjacent pairs of projections, - each of the projections having a pair of radially outer lugs which extend in a circumferential direction into adjacent holding pockets, the radially outer lugs, lugs, which extend from adjacent projections into each of the holding pockets delimiting a radially outer holding surface (166, 168) for in each case one of the rolling bodies of the first plurality of rolling bodies in the corresponding holding pocket, a partially spherical surface on an inner surface of the first ring and respective radially inner, partially cylindrical surfaces which are arranged between the projections of the respective holding pocket making contact with a corresponding rolling body of the first plurality of rolling bodies; and - a second rolling body subunit with a second plurality of rolling bodies and a second cage which is arranged in a second pair of raceways (22, 32) in the inner and the outer bearing ring (20, 30), - the second cage having a second ring with a plurality of axially extending projections, each projection having an axial free end, and holding pockets for the rolling bodies being provided in each case between adjacent pairs of projections, - each of the projections having a pair of radially inner lugs which extend in the circumferential direction into adjacent holding pockets, the radially inner lugs which extend from adjacent projections into each of the holding pockets delimiting a radially inner holding surface (176, 178) for in each case one of the rolling bodies of the second plurality of rolling bodies in the corresponding holding pocket, a partially spherical surface on an inner surface of the second ring and respective radially outer, partially cylindrical surfaces which are arranged between the projections of the respective holding pocket making contact with a corresponding rolling body of the second plurality of rolling bodies; and - the free ends (61, 71) of the projections (64, 74) of the first and the second cage (60, 70) facing one another.