The resonance energy transfer between exciton states in a system comprised of two semiconductor quantum dots is studied theoretically. A model Hamiltonian is constructed to describe the influence of the laser pulse, Coulomb interaction, the static Stark effect, and the relaxation of exciton states on the dynamics of the system. Specific calculations of the efficiency of energy transfer under different excitation conditions and different positions of energy levels are exemplified. It is shown that the transfer process can be controlled by shifting the levels in a constant electric field.