We applied the formalism of double-time Green's functions to the problem of electron transfer from donor (D) to acceptor (A) through large macromolecules. The finite size of a system does not allow the use of momentum representation. For a tight-binding (Huckel-like) Hamiltonian we obtained the Dyson equation. The equation for Green's functions is linear and does not require one to go to higher order ones, which makes analysis of large protein molecules quite feasible. In this paper we analyze the structure of important double-time correlation functions, which will allow us to investigate time-dependent features of long-range electron transfer. We find explicit solutions of Dyson equations for some special cases. Our next paper will be dedicated to a graphical technique which will provide a useful tool to investigate the general case of large macromolecules.