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In this paper it is presented a methodology to assess the transient stability of an electric power system using trajectory sensitivity analysis. This approach studies the variations of the system variables with respect to the small variations in initial conditions and parameters. Trajectory sensitivity functions of the post fault system with respect to relevant parameters are evaluated. The developed technique is combined with an accurate, flexible and efficient hybrid method that allows detailed modelling of the different devices of the power network, the simulation of distinct contingency scenarios, as well as the suitable identification of the different modes of instability. Moreover, it indicates unequivocally the set of the critical machines and allows to easily evaluate the transient stability margin and the critical clearing time.