The invention relates to a hydraulic wheel set press for the simultaneous pressing of two wheel (1, 2) or brake disks on a wheel axis (3) having a frame construction (4) mounted on a base (5), said frame construction being comprised of two identical vertical press stands (6, 7) connected to one another in a fixed manner at a mutual distance via horizontal traverses (8, 9). The press stands (6, 7) each have a housing (10, 11) serving to accommodate a centering cylinder (12) engaging the wheel axis (3) on one end (14 15). In addition, a press cylinder (13) is provided concentrically to the centering cylinder (12). said press cylinder engaging the wheel (1, 2) or brake disk to be pressed, as well as control devices (22) for loading each of the two cylinders (12, 13) with a pressure medium. Measurement devices (20, 21) are provided on the base (5) that detect the lift of each of the cylinders (12, 13) and are connected to a control device (22) provided for regulating the loading of the cylinders (12, 13) with pressure medium as a function of the lift thereof.