Abstract: The invention is a system and process for pumping fluids in lines, comprising using, on the lines, a pump with at least two alternating fluid pumping units. Each pumping unit (PU1, PU2) comprises a cylinder (2) and a piston (1) alternately displaceable in the cylinder under the action of a power source (M), under the control of a control device (PC), with, for both pistons, imposed displacement functions (f(t), g(t)) suitably phase-shifted in relation to one another so as to obtain a first operating mode corresponding to substantially constant delivery rate. This pump is operated in the same circuit according to the complementary second operating mode corresponding to a substantially constant intake rate by inversion of the direction of displacement of the pistons so as to apply to the pistons displacement functions (−f(t), −g(t)) symmetrical to those corresponding to the first operating mode.