a steering fork of the bicycle the outer wheel portion 20 is adapted as will be described below for rotation about the normally non rotating concentric inner wheel portion 30 the inner wheel portion 30 pivotally engages the extension arm 40 which terminates at a free end 42 the extension arm 40 in the preferred embodiment is a pair of arms 40 u2032 and 40 u2033 which act in unison the free end 42 of the extension arm 40 engages a singular wheel mounting axle 60 adapted for receiving the wheel mounting frame at the axle 39 s extremities 62 a biasing means 70 engages the extension arm 40 and abuts a surface 32 of the inner wheel portion 30 the biasing means 70 is enabled by its elastic nature and strength for supporting the wheel mounting axle 60 which in turn supports part of the weight of the conveyance that is carried by the wheel and for absorbing mechanical shocks to the wheel it is of particular interest and novelty to realize that the self suspending wheel apparatus 10 and the frame 50 to which it is mounted are joined together solely by the singular wheel mounting axle 60 in a preferred embodiment of the present invention as shown in fig1 the outer wheel portion 20 is represented by a hub housing as shown in the figures the outer wheel portion 20 is joined to the inner wheel portion 30 by a pair of circular bearing assemblies 80 providing inner 82 and outer 84 bearing races.