Optimal control theory is applied to the design of an active suspension system for a car on a random road. The performance index employed is a weighted sum of mean-squared values for the body forces, tyre dynamic deflections and relative wheel travels. The speed-dependent time delay between the road disturbance inputs is shown not to affect the optimal control law which is linear and time invariant. An explicit expression is obtained for the performance index. The practical realization of the optimal system is discussed and its characteristics compared with those of a conventional passive type suspension system.