This work deals with a dynamic dial-a-ride problem with time window constraints. In particular, new unplanned requests for service may arise at a vehicle stop and the driver must decide in real-time whether to accept or reject them.For this problem, we have developed a two-phase insertion algorithm based on route perturbations: the first phase, which is run off-line when the vehicle moves between two successive stops, aims at creating a feasible neighborhood of the current route; while the second phase, which is run in real-time every time a new request occurs, inserts, when possible, the delivery stop of the new customer in the current route.