A counter-rotating machine, such as a positive displacement pump having a pair of meshed, non-contacting helical screws (10,12), subjects its rotating members to axial and radial thrust forces when used for such purposes as compression of liquid or gaseous phase fluids while transporting them through a pump cavity (11,13). Each helical screw (10,12) has a shaft (17,17') which is actively suspended at opposite ends (11a,11b) of the pump cavity by a servo-controlled magnetic bearing assembly (19) and a servo-controlled rotary drive motor (20). Both bearing assemblies and drive motors are mounted on the outside of the pump cavity (11,13). Opto-electric angular position sensors (250) provide synchronization between radial orientation of the drive motors. The bearing assemblies and drive motors conjugately provide axial stabilization and radial centering of the helical screws during volumetric compression of aspirated liquid or gaseous phase fluids.