Dynamic traffic assignment provides a valuable means to investigate congested road networks and hence to develop traffic management measures for them. These methods have two distinct components: a traffic model, which represents the propagation of vehicles through the network, and a route choice model, which represents the drivers' response to the conditions that they encounter. We investigate the properties and suitability of various traffic models for use in dynamic assignment using an analysis based upon a dynamic extension of Wardrop's equilibrium condition for route choice. We consider various requirements of plausible traffic behaviour, notably conservation of traffic and dependence only on traffic downstream, and establish the crucial importance of the latter in the present context. General analytical results are complemented by calculations for simple example networks: this shows that the deterministic queueing and the kinematic wave models of traffic are suitable for this use, but that several other traffic models that are used widely give rise to dynamic assignments that have unacceptable characteristics.