A pump system for use in with a downhole pipe string has a pump comprising at least one cylinder with at least one piston inside the cylinder, the movement of the piston causing fluid to be drawn into the pump through a pump inlet before being pushed out through a pump outlet. The pump is housed in a tube having a cammed surface formed by internal wall of the tube, and the piston has a cam follower such that rotation of the piston relative to the tube causes the piston to move relative to the cylinder. Further, a pump system is shown which has two or more such pumps arranged along the downhole pipe string, the pump outlets feeding into a common manifold. The strokes of the piston or pistons of one pump may be out of step with the strokes of the piston or pistons of another pump such that the outlet stream is more uniform.