Energy transfer in periodic arrays of optically active ions is investigated. It is assumed that the transfer of excitation between ions takes place incoherently via a one-phonon process where the wavelength of the phonon is large in comparison with the inter-ion spacing. It is pointed out that the energy transfer can only occur where there is a mismatch in energy between the excited states of the two ions. The energy diffusion constant is calculated in an effective medium approximation assuming a Gaussian lineshape with no correlation between the excited state energies of neighboring ions, The temperature dependence of the diffusion constant is established for cubic lattices with nearest-neighbor transfer. Energy transfer in one-dimensional arrays with nearest-neighbor transfer is studied using an extension of the coherent exchange approximation developed for random ferromagnets. The coherent exchange approximation reproduces the asymptotic non-diffusive behavior found in numerical studies of fluorescence line narrowing in one-dimensional systems. (C) 2002 Elsevier Science B.V, All rights reserved.