The kinetics of the excitation quenching by acceptors in the presence of excitation migration over the donors is determined on fractals. We have used the Burshtein approach to determine the dynamics of the excitation hopping mechanism. The results were compared with the experimental study of electronic energy transfer of a two-component system [rhodamine 6G (R6G) as the donor and malachite green (MG) as the acceptor] adsorbed on a silica gel 200 surface. Samples ranging from high acceptor-low donor concentrations (the Förster limit) to the opposite regime were studied. The one-parameter fitting procedure yields a fractal dimension of 2.3 ± 0.03. The same dimension has been previously obtained by us in both depolarization measurements and in direct energy transfer experiments.