A method and device establishes trajectory planning, predictions and guidance so as to obtain the satisfaction of a time constraint (RTA). This objective is achieved by undertaking a computation of a trajectory up to the point where the flypast time constraint applies, on the basis of a profile of altitude and speeds, and then by computing the profile of speeds and altitudes making it possible, throughout the computed trajectory, to comply with the RTA. The method is also a method for readapting the trajectory and the vertical profile when during a mission, the data outside the aeroplane have caused the time predictions to drift and the constraint is no longer complied with under the initial speeds and trajectory assumptions.