A system for steering the direction of a borehole advanced by cutting action of a rotary drill bit by periodically varying the rotation speed of the drill bit. The steering system comprises a motor disposed in a bent housing subsection and operationally connected to a drill string and to the drill bit. The rotation speed of the drill bit is periodically varied by periodic varying the rotation speed of the motor or by periodic varying the rotation speed of the drill string. Periodic bit speed rotation results in preferential cutting of material from a predetermined arc of the borehole wall which, in turn, resulting in borehole deviation. Both the drill string and the drill motor are rotated simultaneously during straight and deviated borehole drilling.