Castor oscillations are of prime importance in many situations, from the simple tea-trolley to towed vehicles, the landing wheels of aircraft, and the motorcycle instability problem of ‘speed wobbles’. This paper sets out a mechanism of castor instability based on the lateral flexibility in the wheel support. In the case of a motorcycle this is the flexibility in the front fork/wheel system.For small amplitude oscillations the equations of motion are shown to be coupled ordinary differential equations which contain terms representing a relay switching function. These equations are solved numerically for many parameter variations. Close agreement is obtained with observed amplitudes and frequencies, and with the oscillation characteristics. For certain sets of parameters the numerical solutions are also found to agree well with the predicted solutions obtained using an analytic technique.From the results it is very clear that the most important parameter affecting stability is lateral stiffness, and a new motorcycle front fork of high lateral stiffness is described. This fork has already achieved success on the road, test track and race track.