Abstract: A sway capable bicycle has a bicycle frame firmly mounted on a sway-capable upper base mounted on a lower base and which has resilient members connecting each corner of the base support to the corresponding corner of the upper base.

Abstract: A sway capable stationary bicycle system comprises a bicycle frame with an inertial wheel firmly mounted on a sway capable base comprising a base core which can sway side to side relative to the upright equilibrium plane of the bicycle frame by rotating on two hinges mounted on a base support which rests on the ground and which has 4 pneumatic or hydraulic struts or elastic air-filled chambers connecting each corner of the base support to the corresponding corner of the base core above. A rider can mount the bike frame which comprises further a saddle, a pedal and crank arm mechanism with a sprocket driving a chain which in turn drives the inertial wheel by means of a concentric gear. The entire rider plus bicycle system exhibits an unstable equilibrium at the upright position which challenges the rider to sway his body from side to side to counterbalance the swaying of the bicycle itself in a similar manner to a real road bicycle.