Braking and/or clamping apparatus for attachment to a slide guided by at least one guide rail, with - the apparatus comprising a housing, at least one wedge shifting transmission (92, 107, 96), at least one rolling-contact member and at least one cage per wedge shifting transmission (92, 107, 96), - the apparatus further comprising at least one frictional restraining means actuatable via wedge shifting transmission (92, 107, 96) and having at least one pressing member mounted inside housing and adapted to be urged onto guide rail, - said wedge shifting transmission (92, 107, 96) being movable in one direction by means of spring force and/or pneumatic or hydraulic compressive force for loading frictional restraining means, and being movable for relief in the opposite direction through pneumatic or hydraulic compressive force by means of at least one piston (63, 71, 81), - said piston or pistons (63, 71, 81) being disposed in at least one multiply stepped through-bore (23, 34, 77, 87) of housing, with the center line of said through-bore oriented in parallel with the longitudinal guidance direction, - the shifting wedge of wedge shifting transmission (92, 107, 96) acting upon pressing member through said at least one rolling-contact member, and - said rolling-contact member or members mounted inside the cage, said cage movable in the longitudinal guidance direction of the piston or pistons (63, 71, 81), characterized in that - the cage is adapted to be mounted in a housing bore aligned transversely of the longitudinal guidance direction by being pushed thereinto, said housing bore intersected or crossed by a connecting bore which is a part of through-bore (23, 34, 77, 87), and - the connecting bore has a diameter smaller than 30 % of the diameter of a spring storage bore, which latter bore is a part of through-bore (23, 34, 77, 87). - the apparatus comprising a housing, at least one wedge shifting transmission (92, 107, 96), at least one rolling-contact member and at least one cage per wedge shifting transmission (92, 107, 96), - the apparatus further comprising at least one frictional restraining means actuatable via wedge shifting transmission (92, 107, 96) and having at least one pressing member mounted inside housing and adapted to be urged onto guide rail, - said wedge shifting transmission (92, 107, 96) being movable in one direction by means of spring force and/or pneumatic or hydraulic compressive force for loading frictional restraining means, and being movable for relief in the opposite direction through pneumatic or hydraulic compressive force by means of at least one piston (63, 71, 81), - said piston or pistons (63, 71, 81) being disposed in at least one multiply stepped through-bore (23, 34, 77, 87) of housing, with the center line of said through-bore oriented in parallel with the longitudinal guidance direction, - the shifting wedge of wedge shifting transmission (92, 107, 96) acting upon pressing member through said at least one rolling-contact member, and - said rolling-contact member or members mounted inside the cage, said cage movable in the longitudinal guidance direction of the piston or pistons (63, 71, 81), - the cage is adapted to be mounted in a housing bore aligned transversely of the longitudinal guidance direction by being pushed thereinto, said housing bore intersected or crossed by a connecting bore which is a part of through-bore (23, 34, 77, 87), and - the connecting bore has a diameter smaller than 30 % of the diameter of a spring storage bore, which latter bore is a part of through-bore (23, 34, 77, 87).