The present invention generally provides a wheel replacing traction assembly which uses, for propulsion, a longitudinally extending endless track disposed around and cooperating with a sprocket wheel, idler and/or road wheels and a supporting frame. The endless track generally comprises an inner wheel-engaging surface and an outer ground-engaging surface, the latter being provided with traction lugs. The outer surface further comprises at least one laterally extending portion which also extends along the circumference of the track; the traction lugs located on this laterally extending portion being generally higher than the traction lugs located on the remainder of the outer surface.