A brake assembly, in particular of a hydraulic wheel drive, comprising a disk package formed of a plurality of outer disks and corresponding inner disks, and compressible a piston assembly for braking. A first hydraulic cycle acts on the piston assembly for driving braking and a second hydraulic cycle acts on the piston assembly for parking braking. The piston assembly includes a driving brake piston which contacts the disk package and is able to be pressurized by the first hydraulic cycle and also able to be pressurized by an adjacent separate parking brake piston interacting with the second hydraulic cycle.