The method of binary collision expansion has been employed to obtain series developments in powers of the scattering length between two particles for double-time-temperature-dependent Green's functions of statistical mechanics. We have studied the cases of Bose and Fermi statistics as well as the case of a Bose system in the presence of a condensed phase, and have established rules for computation of the successive terms of expansion with the aid of diagrams. The present method is applicable to many particle systems with strong and short-ranged mainly repulsive two-body interactions.