A two stage pump (2′, 4′), where the high pressure stage (4′) is a gear pump (11, 12), comprises a driving of the other stage (2′) by a support shaft (74), mounted in the driven pinion (12), the shaft (74) being driven by the drive shaft (21), by means of a pair of toothed wheels (77, 79) adjacent to the rest of the stage (4′), which can allow different rotation speeds between the two stages (2′, 4′). The support shaft (74) may be supported by stops and hydrodynamic bearings, directly integrated and lubricated in the driven pinion, which make the design lighter and more compact. The shaft (74) and the toothed wheels (77, 79) ingeniously transmit the loads from the stage (2′) to the stage (4′) in such a way as to cancel out the usual hydraulic loads, stemming from pressure, and mechanical, forces stemming from rotational drivings on the driven pinion (12).