We analyze the out of plane hopping in models of layered systems where the in-plane properties deviate from Landau's theory of a Fermi liquid. We show that the hopping term acquires a nontrivial energy dependence, due to the coupling to in-plane excitations, and the resulting state, at low temperatures, can be either conducting or insulating in the third direction. The latter is always the case if the Fermi level lies close to a saddle point in the dispersion relation.