  We present a general model allowing one to calculate the distribution
function of energetic particles in the interstellar medium, and hence any
relevant nuclear reaction rate, for any given time-dependent injection
function, as well as in situations when the propagation coefficients themselves
are non stationary. We review and provide physical interpretation of general
formal solutions of a propagation equation taking into account energy losses,
nuclear destruction and escape. Both one-zone and extended models are
investigated. Our main goal is to provide standard and general tools for
subsequent use in nuclear astrophysics, notably to calculate the gamma-ray
emission and spallation rates associated with energetic events and specific
acceleration mechanisms. Considering the stationary limit of the model, we show
that only time-dependent calculations can probe the density dependence of the
physical processes under study, while steady-state models can \emph{in
principle} only give information about density-independent processes.
