the working chamber 11 an axial bore 12 communicates with a chamber 13 which in turn communicates through a line 14 with the bore 10 of the cylinder bushing 9 the axial bore 12 can be closed by a valve member 15 loaded in the direction of the working chamber 11 the connecting line 14 can be connected in sequence with pressure lines 20 terminating in the bore 10 through an annular groove 17 on the periphery of the pump piston 8 and through an axially oriented distributor groove 18 which is connected thereto the pressure lines 20 are evenly distributed about the cylinder bore 10 and correspond to the number of cylinders of the internal combustion engine to be supplied with fuel at each pressure stroke of the pump piston 8 fuel is delivered through the axial bore 12 the chamber 13 the connecting line 14 and the distributor groove 18 to one of the pressure lines 20 during the suction stroke fuel flows from a suction chamber 24 through a supply line 23 terminating in the bore 10 and through one longitudinal groove 22 of a plurality of such grooves into the working chamber 11 the grooves 22 are equal in number to the number of cylinders of the engine and are similarly configured on the periphery.