A safety device limits the pressure in an axial-piston compressor with variable piston displacement. The compressor has as wobble plate or swash plate whose tilt angle can be variably controlled by the pressure differential between the high pressure in the discharge pressure zone and the pressure in the piston-drive chamber. The safety device consists of a valve arranged in a connector channel between the discharge pressure zone and the pressure zone of the piston-drive chamber. When the discharge pressure exceeds a given pressure limit, the safety device responds by allowing an increased flow of pressure medium from the discharge pressure zone to the piston-drive chamber. The influx of pressure medium into the piston-drive chamber causes a reduction of the tilt angle of the swash plate or wobble plate.