Abstract: A brake system for full-track vehicles having a shift gear (3) and superimposed steering gears (8) situated across the longitudinal axis (F) of the vehicle and two summing transmissions (5) situated near the two transmission output shafts (54). The shift gear and the superimposed steering gears, the same as the summing transmissions and other gears and devices, are situated as assemblies (A, B, C, D, E, P) in or upon a common housing and form a common transmission system. The brake system consists, in a first embodiment, of a secondary retarder (1) and a friction brake (2), both situated before the summing transmission. In normal braking, the secondary retarder (1) is first pressurized with the brake actuation device and only later is the friction brake (2) pressurized. In a second example of use a primary retarder (7) and a secondary retarder (1) are situated in the area of the shift gear, and the braking down to stoppage results from one or more shift brakes (B1, B2, B3) in a second function.