A variable capacity wobble plate compressor includes a wobble plate (36) in the crank chamber (7) for adjusting the piston stroke; a control valve (45) for controlling the chamber pressure in the crank chamber to adjust the angle of the wobble plate; a pressure sensor (53); a rotary speed sensor (56); a heat load sensor (61); and/or a vibration sensor (62); and a control unit responsive to a signal from at least one of the sensors for controlling the control valve to prevent the compressor from entering an unstable zone.