An engine-propelled monowheel vehicle comprises two wheels, close together, that circumscribe the remainder of the vehicle. When the vehicle is moving forward, the closely spaced wheels act as a single wheel, and the vehicle turns by leaning the wheels. A single propulsion system provides a drive torque that is shared by the two wheels. A separate steering torque, provided by a steering motor, is added to one wheel while being subtracted from the other wheel, enabling the wheels to rotate in opposite directions for turning the vehicle at zero forward velocity. The vehicle employs attitude sensors, for sensing roll, pitch, and yaw, and an automatic balancing system. A flywheel in the vehicle spins at a high rate around a spin axis, wherein the spin axis is rotatable with respect to the vehicle's frame. The axis angle and flywheel spin speed are continually adjustable to generate torques for automatic balancing.