Abstract We extend previous treatments of small amplitude damped collective motion in fermion systems. The equations of motion for Green′s function are solved in an iterative manner. The Brueckner-Hartree-Fock mean field is improved by infinitesimally advanced terms corresponding to fast hole-hole collisions. Non-equilibrium excitations lead to damped collective motion with a redistribution of the occupation probabilities according to energy conservation. The damping is due to slow collisions, which are influenced by the past collision history of the system. A criterion for the stability of motion is formulated. The time evolution of the entropy is explicitly calculated. In the adiabatic limit of slow temporal and spatial variation the Landau theory of Fermi liquids is recovered. The theory is applied to a model system which shows the generic features of a fermion system. It is shown that the memory time is inversely proportional to the bandwidth of single particle states contributing to the damping process.