The Lifshitz formula for dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. The principal nonlocality of poor conductors is related to the finite screening length of the penetrating field and collisional relaxation; at low temperatures the role of collisions plays the Landau damping. Spatial dispersion makes the theory self-consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures Casimir-Lifshitz entropy disappears as T in the case of degenerate plasma and as T-2 for the nondegenerate one.