Abstract: Vacuum pump of reciprocating piston and cylinder type. Cylinder is stepped to have front large diameter portion and rear small diameter portion. Piston has enlarged head portion sliding in front portion of cylinder and rear portion sliding in rear portion of cylinder. Front end of cylinder is closed to form high vacuum pumping chamber swept by front face of piston head. Gas enters the high vacuum pumping chamber through side wall of cylinder and can be exhausted through exhaust valve in closed front end of cylinder. Rear annular face of piston head sweeps lower vacuum chamber in cylinder behind the piston head. A gas transfer passage extends through cylinder wall from front end of high vacuum pumping chamber to port in cylinder wall so as to transfer gas from high vacuum chamber to lower vacuum chamber when piston approaches end of forward stroke. Gas is transferred through transfer duct at pressures lower than required to open the exhaust valve.