A roller bearing for linear movements has two guide members arranged coaxially relative to each other between which there are provided races for roller members extending in the longitudinal direction. The roller members are biased in radial direction by at least one elastic element. The races for the roller members are shaped as guide surfaces directly at the two guide members, and the elastic element is provided radially offset with regard to the guide surfaces and acts by means of webs only indirectly onto these surfaces, by being subjected to a radial clamping force of a further annular element.