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We solve the problem of constructing consistent first-ordercross-interactions between spin-2 and spin-3 massless fields in flat spacetimeof arbitrary dimension n > 3 and in such a way that the deformed gauge algebrais non-Abelian. No assumptions are made on the number of derivatives involvedin the Lagrangian, except that it should be finite. Together with locality, wealso impose manifest Poincare invariance, parity invariance and analyticity ofthe deformations in the coupling constants.Comment: LaTeX file. 29 pages, no figures. Minor corrections. Accepted for  publication in JHE

Consistent couplings between spin-2 and spin-3 massless fields