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We prove the local Gross-Prasad conjecture for generic L-packets ofrepresentations of special orthogonal groups. The proof uses the same resultfor tempered L-packets proved in a preceding paper, and irreducibility resultsfor the induced representations of whose the elements of the L-packets areLanglands quotients.

La conjecture locale de Gross-Prasad pour les groupes sp\'eciaux orthogonaux: le cas g\'en\'eral