A hydrostatic pump or motor unit having a rotating cylinder biased into contact with a valve surface in proportion to separating forces to maintain sealing contact without excessive pressure. In an axial piston type hydrostatic unit, the rotating cylinder block engaging a fixed annular valve plate and the swash plate reciprocate the pistons in the cylinders to deliver fluid from the cylinders through the valve plate. A biasing motor between the cylinder block and a member axially fixed relative to the valve plate and a control system to provide a biasing control pressure provides a biasing force varying as a function of the separating force between the valve plate and cylinder block. In one arrangement the biasing motor has an internal cylindrical surface on the cylinder block and an external cylindrical surface on a fixed portion of the housing with a pair of annular pistons therebetween, one engaging in abutment on the cylinder block and the other engaging in abutment on the fixed housing portion to form a motor chamber supplied with biasing control pressure fluid to provide an auxiliary bias proportional to this pressure. In another arrangement the inner cylindrical surface is formed on the shaft rotating with the cylinder block. The biasing control system in one modification provides a biasing pressure proportional to speed and in another modification proportional to speed, power system pressure and displacement. A one or two step speed governor is mounted in the cylinder block.