A hydraulic motor (2) with a braking device (8), is acted upon by means of a control fluid via a brake release line (6). The brake release line (6) is used to allow a continuous flushing flow of control fluid through the hydraulic motor at the same time as the release of the brake. The braking device (8) is connected to the casing of the hydraulic motor (2). An outlet opening (12) of the hydraulic motor (2) leads via a leakage-oil line (13) to the tank for the control fluid. In a hydraulic travel drive with a closed hydraulic circuit, the brake release line (6) can be connected to the shut-off device (4) for the servo adjustment system of the variable-displacement pump (1), and the leakage-oil line (13) of the hydraulic motor (2) can lead to the tank for the entire hydraulic fluid in the system. Since the control fluid coming from the tank for the hydraulic fluid is always cooler than the hydraulic fluid used to drive the hydraulic motor (2) and circulating in the closed circuit, a cooling effect on the hydraulic motor (2) is obtained.