The invention relates to a brake system for braking wheels of a motor vehicle that rotate about axle spindles, with a brake caliper fixing device, which comprises an axle-side support (1) that can be attached to the vehicle axle, and comprises a brake-side support (3), which can be detachably attached to support (1) by means of bolts (2) and which serves to accommodate the brake caliper (4) of the brake (5). Axial and radial contact surfaces (6, 7) of the axle-side support (1) or of the brake-side support (3) are essentially located in one and the same axial or radial plane, the axial contact surface separates with the radial contact surface, and the supports, on the contact surfaces thereof, are held against one another by means of at least two axially parallel bolts (2).