This article deals with the problem of real-time modelling and prediction of motorway traffic. Conditional independence relationships and ideas of Bayesian forecasting are proposed leading to the employment of dynamic state-space models, with optimal state estimation coming from the Kalman filter. Models, based on classical differential equations, which incorporate representations of the network topology are derived and are implemented in a state-space framework. The model is applied to several road networks in The Netherlands from which encouraging preliminary results are obtained.