An apparatus for steerable rotary drilling of a borehole having a wall in the earth comprising, a mandrel, having a central opening there through for the passage of drilling fluids, said mandrel having a lower connection for operatively connecting to a drill bit structure, said mandrel having an upper connection for operatively connecting to a drill string above said apparatus, and the mandrel having an intermediate portion, an outer housing surrounding longitudinal extent of said mandrel intermediate portion, a differential displacement drive within the outer housing, one or more pairs of radially-extensible, opposed side-force exerting elements controlled by said differential displacement drive to provide for side force exertion against the said borehole wall, said drive including a pair of pistons for activating each pair of radially-extensible opposed side-force elements, one or more displacement transducers for said pair of pistons, control valves within said outer housing for fluid pressure control of said differential displacement drive, and sensing, control and power supply elements to control operation of said control valves, to steer drilling in a desired direction by selective operation of said side force exerting elements.