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. To determine the relevant quasi-equilibrium configuration at time t from given initial conditions, such slow evolution is often approximated in terms of adiabatic evolution. Here we focus on the slow process of evolution induced by dynamical friction of a spherical stellar system (the host galaxy) on a minority component of “satellites” (distributed in a spherical shell), to determine to what extent an adiabatic description might be applied.