Abstract: The braking device has several groups of brakes (22 to 25), which can be applied separately by a control device (35) and each of which has at least one friction brake (16 to 19). The control device (35) controls the application of the groups of brakes (22 25) depending on their wear condition and temperature, such that application of the least-worn group of brakes (20 to 25) is favored, whereby the friction brakes (16 to 19) of each of the applied groups of brakes (22 to 25) quickly attain an advantageous temperature range with respect to minimum wear, and are maintained in such range. The entire braking of the rail vehicle or train (1) is always maintained in addition in agreement with a braking requirement signal for the rail vehicle or train (1). This produces equal wear of all brake shoes (20), whereby the friction brakes (16 to 19) are always operated at a temperature range most advantageous for wear and with the most wear-advantageous pressure with moderate braking strength.