A double-acting brake assembly comprising a drum mounted on a rotary shaft, a brake band with looped ends surrounding the drum, and actuator means to displace ends of the band toward one another, is provided with a mounting bracket having spaced reaction surfaces which cooperate with the ends of the band to permit the band to wrap onto the drum for braking the drum when rotating in either the clockwise or counterclockwise directions. The reaction surfaces extend widthwise of the band adjacent the periphery of the drum, and a pair of guide surfaces extend alongside the ends of the band for aligning the band axially of the drum. In one embodiment, the bracket has an L-shaped crosssection with a flange overlying the drum and the reaction and guide surfaces are provided by the edges of an aperture in the flange. Other forms of brackets, including a bracket combined with a dust cover, are also disclosed. A preferred form of actuator includes a flexible sheath and cable assembly having one end connected to an operating lever and the other end connected to the ends of the band. The actuator draws the looped ends of the band together to engage the band with the drum, but allows lost motion between the end loops and the reaction surfaces of the mounting bracket. The end loops are free to move against either reaction surface, so that no matter which direction the drum is rotating, it will be the end loop at the leading end of the band which engages a reaction surface, and the trailing end of the band will in every case be free to wrap about the drum to provide a servo or self-energizing braking action. This will provide self-energizing braking on both forward and reverse rotation of the drum.