  Many astrophysical problems, ranging from structure formation in cosmology to
dynamics of elliptical galaxies, refer to slow processes of evolution of
essentially collisionless self-gravitating systems. In order to determine the
relevant quasi-equilibrium configuration at time t from given initial
conditions, it is often argued that such slow evolution may be approximated in
terms of adiabatic evolution, for the calculation of which efficient
semi--analytical techniques are available. Here we focus on the slow process of
evolution, induced by dynamical friction of a host stellar system on a minority
component of "satellites", that we have investigated in a previous paper, to
determine to what extent an adiabatic description might be applied. The study
is realized by comparing directly N--body simulations of the stellar system
evolution (in two significantly different models) from initial to final
conditions in a controlled numerical environment. We demonstrate that for the
examined process the adiabatic description is going to provide incorrect
answers, not only quantitatively, but also qualitatively. The two classes of
models considered exhibit generally similar trends in evolution, with one
exception noted in relation to the evolution of the total density profile. This
simple conclusion should be taken as a warning against the indiscriminate use
of adiabatic growth prescriptions in studies of structure of galaxies.
