The use o f modem estimation theory to track the time-varying dynamics of a motorcycle suspension system is investigated. It is shown using software simulations and a test rig comprised of an analogue computer that a modified recursive least squares algorithm which incorporates a fault detection scheme is a suitable approach. The fault detection scheme incorporated in the modified algorithm detects system changes by monitoring the statistical properties of the estimators prediction error sequence. A mass, spring and damper model is chosen as a simple model with which to represent the dynamics of the suspension system. Initial estimates of the suspension parameters are found from static tests performed on a sample "Formula 1" front suspension unit. These estimates are incorporated into a software simulation and this simulation is used as a platform to examine the performance o f existing parameter estimation techniques and also to develop the modified least squares algorithm. An analogue computer is built as a hardware representation of the system dynamics. The modified algorithm is fine tuned using equivalent force and displacement data from this computer. The modified algorithm is used to track the parameters of this computer. The resulting parameter estimates indicate that the modified algorithm yields estimates which have superior variance and convergence properties than those of estimates obtained using more conventional parameter estimation schemes.