The methodologies developed for the simulation of strong ground motions to estimate the seismic hazard in Mexico City soft soils, and at a rock site in the southeast of Mexico are presented. For both sites a bayessian seismic hazard model is applied. In the former site the Montecarlo simulation technique was utilized to obtain the synthetics. For the latter site the empirical Green function technique is used for this purpose. The main conclusions of the work are: 1) In the Mexico City soft soils case the estimated seismic hazard, computed before the 1985 Michoacan earthquake, successfully predicted the maximum ground motion observations for this event. 2) The incorporation of the potential seismic activity of faults located nearby the site in the southeast of Mexico, has a large impact in the estimated seismic hazard, compared with the results obtained without considering that potential.