This paper addresses the problem of dynamical systems with parameters varying in time (transient systems). A method to predict their behaviour is proposed. This class of transient systems can be seen as the evolution of an ordinary steady system into another ordinary steady system, for both of which the classical theory of dynamical systems holds. The evolution from a steady system to the other is driven by a transient force, which is regarded as a map between the two steady systems. We apply our method to a system which is subjected to a transient excitation, that is neither constant nor periodic, to simulate the effect of switching-on procedures.