A constant velocity joint, comprising: an outer joint part; a ball cage containing one ball in each of a plurality of circumferentially spaced windows in said cage, said ball cage having a first inner partial spherical surface facing a front opening (Rf) of said cage defined by a first radius having a center offset from a ball center, a second inner partial spherical surface facing a rear opening (Rr) of the cage defined by a second radius having the same center offset from said ball center, wherein said first radius is smaller than said second radius, and a transition section between said partial spherical surfaces; an inner joint part having a first partial spherical surface facing a front opening (Rf) of said cage, a second partial spherical surface facing a rear opening (Rr) of said cage, wherein a) there is only a single transition section between said partial spherical surfaces (64, 66) of the ball cage and the inner joint part has a single transition section between said partial spherical surfaces (60, 62) of the inner joint part; and wherein said ball cage spherical surfaces (64, 66) and said inner race spherical surfaces (60, 62) define between them an open space having a predetermined length defined by the overlap of said first inner partial spherical surface of said ball cage and said first partial spherical surface of said inner joint part or b) the inner joint part additionally has a flat cylindrical surface in direct contact with said second partial spherical surface and a transition section in direct contact with said flat cylindrical section and said first partial spherical surface; and wherein said ball cage spherical surfaces (64, 66), said inner joint part first partial spherical surface and said flat cylindrical surface define between them an open space having a predetermined length. an outer joint part; a ball cage containing one ball in each of a plurality of circumferentially spaced windows in said cage, said ball cage having a first inner partial spherical surface facing a front opening (Rf) of said cage defined by a first radius having a center offset from a ball center, a second inner partial spherical surface facing a rear opening (Rr) of the cage defined by a second radius having the same center offset from said ball center, wherein said first radius is smaller than said second radius, and a transition section between said partial spherical surfaces; an inner joint part having a first partial spherical surface facing a front opening (Rf) of said cage, a second partial spherical surface facing a rear opening (Rr) of said cage, wherein a) there is only a single transition section between said partial spherical surfaces (64, 66) of the ball cage and the inner joint part has a single transition section between said partial spherical surfaces (60, 62) of the inner joint part; and wherein said ball cage spherical surfaces (64, 66) and said inner race spherical surfaces (60, 62) define between them an open space having a predetermined length defined by the overlap of said first inner partial spherical surface of said ball cage and said first partial spherical surface of said inner joint part or b) the inner joint part additionally has a flat cylindrical surface in direct contact with said second partial spherical surface and a transition section in direct contact with said flat cylindrical section and said first partial spherical surface; and wherein said ball cage spherical surfaces (64, 66), said inner joint part first partial spherical surface and said flat cylindrical surface define between them an open space having a predetermined length. a) there is only a single transition section between said partial spherical surfaces (64, 66) of the ball cage and the inner joint part has a single transition section between said partial spherical surfaces (60, 62) of the inner joint part; and wherein said ball cage spherical surfaces (64, 66) and said inner race spherical surfaces (60, 62) define between them an open space having a predetermined length defined by the overlap of said first inner partial spherical surface of said ball cage and said first partial spherical surface of said inner joint part or b) the inner joint part additionally has a flat cylindrical surface in direct contact with said second partial spherical surface and a transition section in direct contact with said flat cylindrical section and said first partial spherical surface; and wherein said ball cage spherical surfaces (64, 66), said inner joint part first partial spherical surface and said flat cylindrical surface define between them an open space having a predetermined length.