Electronic excitation energy transfer is studied theoretically within a prototype system of quantum dots using the excitonic representation of the electronic states of two quasi-zero dimensional subsystems, between which the excitation energy is transferred in a process treated as an irreversible kinetic phenomenon. The electron-phonon interaction, included in an approximation going beyond the limits of finite order perturbation calculation, is used when considering the so called uphill and

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... hill excitation transfer processes. The theory is deveped upon utilizing a simplified model of two interacting quantum dots, both coupled to their environment. The theoretical approach is documented by numerical calculations. The results should be relevant to various cases of the electronic excitation energy transfer between quasi-zero-dimensional nanostructures.