It is shown that the Mori theory of relaxation provides a suitable theoretical framework for the study of excitation-relaxation processes of a non-Markoffian kind, provided that the point of view of Nordholm and Zwanzig be adopted. According to their interpretation of the generalized Langevin equation, it is indeed possible to describe the back reaction of an excited thermal bath on the time evolution of a subsystem of interest. Since the equilibrium distribution of the thermal bath of a non-Markoffian system is significantly affected in the course of excitation of the subsystem, it is then possible to evaluate the time evolution subsequent excitation processes of such a system by pulses of finite duration. In other words, the limitations of linear-response theory leading to the second fluctuation-dissipation theorem can be avoided. A general approach, valid even in the case of non-Hermitian dynamical operators and which allows us to build up a generalized equation, is developed. This approach shows, furthermore, that it is possible to replace the thermal bath of a non-Markoffian variable with a chain of variables undergoing relaxation processes of a Markoffian nature. Since in the new Markoffian system, considered in its totality, the relaxation process is completely independent of the excitation one, the time evolution of any variable of the chain can be evaluated for any intensity of the excitation field. This means that even the limitations of the linear response involved by the first fluctuation-dissipation theorem can be avoided. Owing to the formal similarity between the Schrodinger equation and the equation of motion for operators, it is possible, once suitable scalar products among operators are defined, to apply the one approach both to the quantum-mechanical time evolution of an isolated molecule system and to the classical Brownian motion of molecules in liquids. In the former case, the theory developed in the present paper allows us to build up in a rigorous way a “reduced” effective Hamiltonian which results in a wide range of free-relaxations behaviours, including the damped oscillatory and biexponential types. It is then possible to describe in a realistic way the whole excitation-relaxation process and evaluate both the effects of pulse duration and intensity on any kind of decay behaviour.