Path deformation is a technique that was introduced to generate robot motion wherein a path, that has been computed beforehand, is continuously deformed on-line in response to unforeseen obstacles. In an effort to improve path deformation, this paper presents a trajectory deformation scheme. The main idea is that by incorporating the time dimension and hence information on the obstacles' future behaviour, quite a number of situations where path deformation would fail can be handled. The trajectory represented as a space-time curve is subject to deformation forces both external (to avoid collision with the obstacles) and internal (to maintain trajectory feasibility and connectivity). The trajectory deformation scheme has been tested successfully on a planar robot with double integrator dynamics and a car-like vehicle.