The Wightman and Green functions are one of the basic objects of the relativistic quantum field theory in the Minkowski spacetime. The perturbative definition of the Green functions in a large class of models was given using the momentum-space approach. In the causal perturbation theory developed by Epstein and Glaser both the Wightman and Green functions can be defined by taking the so-called weak adiabatic limit. However, its existence has been shown so far only in purely massive theories, the quantum electrodynamics and the massless ϕ4 theory. The aim of the talk is to present the proof of the existence of the weak adiabatic limit in most of the interacting models including an arbitrary model with the interaction vertices of the canonical dimension equal 4. The developed method can be also used to show the existence of the central splitting solution in the quantum electrodynamics.