By considering the traffic assignment problem as a control problem, this paper develops a new realtime route guidance strategy for accurate convergence of the traffic flows to user equilibrium(UE) or system optimum(SO), in the presence of drivers’ response uncertainties. With the new guidance strategy, the drivers make routing decisions based on the route guidance information from junction to junction. Specifically, instead of total travel cost of every route from origin to destination, the travel cost of every alternative link plus the average cost to destination from the next junction corresponding to the alternative link is sent to the drivers at each specific junction. The drivers’ response to the route guidance information is directly modeled by the splitting rates at the junctions, which are simply negatively correlated with the comparison of related cost information and are able to take into account the drivers’ response uncertainties. With the proposed route guidance strategy, in the case of fixed travel demands, the accurate convergence of the traffic flows to a UE is guaranteed in the presence of drivers’ response uncertainties by using La Salle’s invariance principle. When marginal travel cost information, instead of travel cost information, is sent to the drivers, a system optimum can be achieved under a mild condition on the marginal cost function. By considering the traffic assignment problem as a control problem, this paper develops a new realtime route guidance strategy for accurate convergence of the traffic flows to user equilibrium (UE) or system optimum (SO), in the presence of drivers’ response uncertainties. With the new guidance strategy, the drivers make routing decisions based on the route guidance information from junction to junction. on the total travel cost of every route from origin to destination, the travel cost of every alternative link plus the average cost to destination from the next junction corresponding to the alternative link is sent to the drivers at each specific junction. The drivers’ response to the route guidance information is directly modeled by the splitting rates at the junctions, which are simply negative associated with the comparison of relevant cost information and are able to take into account the drivers’ response uncertainties. With the proposed route guidance strategy, in the case of fixed travel demands, the accurate convergence of the traffic flows to a UE is guaranteed in the presence of drivers’ response uncertainties by using La Salle’s invariance principle. When marginal travel cost information, instead of travel cost information, is sent to the drivers, a system optimum can be achieved under a mild condition on the marginal cost function.