We have studied the influence of up to fifth-nearest neighbor interactions on thermal desorption, using a novel kinetic Monte Carlo simulation scheme. It is shown that in many cases the long-range components of the adsorbate-adsorbate attractions can be reduced to an effective pairwise nearest neighbor interaction, which is much easier to handle, both, in theory and simulation. A criterion for the relevance or negligibility of long-range interaction components will be given. Special attention is devoted to the presence of kinetically limited surface diffusion for adsorbates exhibiting long-range lateral interaction. Such systems are shown to be much more sensitive to kinetic influences than systems governed by nearest neighbor interactions, only. (C) 2003 Elsevier B.V. All rights reserved.