Excitation-energy transfer (EET) has been observed to be very rapid from B800 to B850, between two circular aggregates of bacteriochlorophyll molecules (BChls), in the light-harvesting antenna complex LH2 of photosynthetic purple bacteria. This rapid EET cannot be understood within the framework of Förster's formula, since the luminescence spectrum of B800 overlaps little with the absorption spectrum of B850. The present work shows that it can be rationalized on the basis of a recently proposed formula for EET between molecular aggregates. The formula differs from Förster's one when excited states are excitonic at least in one of the donor and the acceptor aggregates with a mutual distance not much larger than their physical sizes, as in the present case. Excited states of B850 are regarded as excitonic, while those of B800 as monomeric. The exciton−phonon coupling was taken into account over all orders for B800 and within a self-consistent second-order perturbation for B850. Calculated rates of the EET are in the range of 10¹¹−10¹² s^-1, increasing weakly with temperature, in good agreement with experiments. We demonstrate that this rapid EET occurs to optically forbidden exciton states of B850, without total transition dipole, due to strong interaction of a transition dipole on a BChl in B800 with those on nearby BChls in B850.