A peristaltic down-hole drilling motor comprises a series of breathing working chambers that are formed between a membrane and a tubular section of the stator of the motor.The rotor comprises a plurality of rollers that are rotatably supported in grooves of a carrier body such that the rollers press the membrane at selected intervals against said tubular section.The working chambers are designed such that during operation of the motor the rollers are actuated to ride upon the membrane in front of the expanding portions of the chambers, thereby rotating the rotor relative to the stator.