A pump has in a housing a revolvable shaft which drives a piston stroke guide body. Drive pistons are provided with piston shoes which run on the guide face of the piston stroke guide body and drive fluid supply pistons of smaller diameter. The pump preferies a fluid separator between lubricating and non-lubricating fluid, like for example, between oil and water, whereof one of the fluids flows through an inner chamber which is provided with inlet and outlet valves while the outer fluid acts in an outer chamber which is open toward the cylinder wherein the fluid supply piston reciprocates. Dead space fillers are provided to prevent losses by compression of fluid and seal means are assembled to prevent leakage of fluid from one into the other of the chambers. The fluid separator may be compressible and expandable within the plastic deformable range of the material whereof it is made. The pump includes sophisticated technologies which necessiated more than half a decade of intensive research and testing but it is now capable of pumping fluid, including water, of several thousand atmospheres of pressure.