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We compute the amplitude for the radiation of massless NS-NS closed string states from the interaction of two moving D-branes. We consider particle-like D-branes with reference to four-dimensional spacetime, in toroidal and orbifold compactifications, and we calculate the relevant world sheet propagators within the moving boundary state formalism. We find no on-shell axion emission. For large inter-brane separation, we compute the spacetime graviton emission amplitude and estimate the average energy radiated, whereas the spacetime dilaton amplitude is found to vanish in this limit. The possibility of emission of other massless states depends on the nature of the branes and of the compactification scheme. (C) 1998 Elsevier Science B.V.