A swash-plate machine for pumping fluids uses dual swash plates in complementary or mirror-image orientation. The vibration that is generated as a reaction to forced nutatory motion imposed on a single swash plate is thereby largely cancelled. Rotated orientation of the divider plate position in one chamber with respect to the other (preferably 90 degrees difference) provides four outputs per revolution instead of the two available from both sides of a single swash plate. Improved bearings for the part-spherical swash plate base permits only oscillatory movement for that part and facilitate better sealing.