A non-pneumatic tire is disclosed where a resilient wheel is mounted on a rim and the wheel has an inner ring, an outer ring and a plurality of flexible webs interconnected between the inner and outer rings. The flexible webs define openings in through the resilient wheel. The stiffness of the inner wheel at a position adjacent to the inner face is different than the stiffness of the inner wheel at a position adjacent to the outer face. This stiffness difference can be accomplished by providing inflated membranes in at least some of the openings or by molding the wheel with an asymmetric parting line. In addition, the wheels could be dynamically controlled by providing magnetically actuable membranes in some of the openings.