Abstract: The rotor of a disc brake apparatus for bicycles comprises a spider that flatwise overlies the outer face of one spoke flange on a wheel hub and is secured by spokes that have their hook portions extending through it and that spoke flange. A flat annular disc has radially inwardly projecting tabs that are secured to the spider and hold the disc in axially spaced relation to the spokes. A U-shaped caliper body straddles an edge portion of the disc. On a shorter leg the body has a fixed brake pad; on its longer leg it carries a movable brake pad that has a compound motion for self-energization. The body is movable in directions parallel to the wheel axis and is carried, in part, by a cup-shaped adapter coaxial to the wheel shaft and confined between a bearing cone for the wheel and an adjacent frame portion. Portions of the body straddle an elongated frame member to confine the body against rotation around the adapter.