  The paper deals with a multiple species Lotka-Volterra model with infinite
distributed delays and feedback controls, for which we assume a weak form of
diagonal dominance of the instantaneous negative intra-specific terms over the
infinite delay effect in both the population variables and controls. General
sufficient conditions for the existence and attractivity of a saturated
equilibrium are established. When the saturated equilibrium is on the boundary
of $\R^n_+$, sharper criteria for the extinction of all or part of the
populations are given. While the literature usually treats the case of
competitive systems only, here no restrictions on the signs of the intra- and
inter-specific delayed terms are imposed. Moreover, our technique does not
require the construction of Lyapunov functionals.
