A braking and/or clamping apparatus associated with a slide unit and guided along at least one rail, - said apparatus accommodated in a housing and comprising at least one frictional inhibiting mechanism (51, 151) adapted to be actuated via a wedge-type transmission (50, 150), said mechanism comprising at least one pressure member (54, 154) adapted to be urged against rail and/or friction jaws (53, 153), - said wedge-type transmission members (45, 145, 154, 71, 91, 92) being moved by means of extraneous energy and adapted to be moved by means of least one actuator (60, 160) or by means of a spring system for each loading and relieving of said individual friction inhibiting mechanisms (51, 151) in each direction of loading and relief, said spring system comprising at least one spring element (88, 98), and - said wedge-type transmission (50, 150) comprising at least one cage mounted for displacement between at least one pressure member (54, 154) and/ or said friction jaws (53, 153) and at least one roll-off zone facing the housing or a supporting element (45, 145) disposed inside the housing, - characterized in that said at least one cage has at least one transverse opening extending transversely to its direction of displacement, said cage having therein a plurality of rolling elements (91, 92), said plurality comprising two or multiples of two, and said rolling elements contacting each other in a side-by-side relationship and in a direction transverse to the direction of displacement, - in that the movable part and the longitudinal guide portion of actuator (60, 160) include a wedge angle of 0.2 to 5 degrees of an angle relative to the direction of slide displacement, - in that the housing-side roll-off zone or the support element (45, 145) has an end surface facing cage and comprising at least in portions thereof a planar surface or a groove oriented parallel with the direction of displacement of the movable part of said actuator and/or the longitudinal guide element thereof, and - in that pressure member (54, 154) has a roll-off surface of which the normal or centre line is oriented at right angles to the direction of slide displacement. - said apparatus accommodated in a housing and comprising at least one frictional inhibiting mechanism (51, 151) adapted to be actuated via a wedge-type transmission (50, 150), said mechanism comprising at least one pressure member (54, 154) adapted to be urged against rail and/or friction jaws (53, 153), - said wedge-type transmission members (45, 145, 154, 71, 91, 92) being moved by means of extraneous energy and adapted to be moved by means of least one actuator (60, 160) or by means of a spring system for each loading and relieving of said individual friction inhibiting mechanisms (51, 151) in each direction of loading and relief, said spring system comprising at least one spring element (88, 98), and - said wedge-type transmission (50, 150) comprising at least one cage mounted for displacement between at least one pressure member (54, 154) and/ or said friction jaws (53, 153) and at least one roll-off zone facing the housing or a supporting element (45, 145) disposed inside the housing, - characterized in that said at least one cage has at least one transverse opening extending transversely to its direction of displacement, said cage having therein a plurality of rolling elements (91, 92), said plurality comprising two or multiples of two, and said rolling elements contacting each other in a side-by-side relationship and in a direction transverse to the direction of displacement, - in that the movable part and the longitudinal guide portion of actuator (60, 160) include a wedge angle of 0.2 to 5 degrees of an angle relative to the direction of slide displacement, - in that the housing-side roll-off zone or the support element (45, 145) has an end surface facing cage and comprising at least in portions thereof a planar surface or a groove oriented parallel with the direction of displacement of the movable part of said actuator and/or the longitudinal guide element thereof, and - in that pressure member (54, 154) has a roll-off surface of which the normal or centre line is oriented at right angles to the direction of slide displacement.