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This paper is concerned with a viscoelastic equation of Kirchhoff type withacoustic boundary conditions in a bounded domain of $\mathbb{R}^{n}.$ We showthat, under suitable conditions on the initial data, the solution existsglobally in time. Then, we prove the general energy decay of global solutionsby applying a lemma of P. Martinez, wihch allows us to get our decay result fora class of relaxation functions wider than that usually used.

General enegy decay for a viscoelastic equation of Kirchhoff type with acoustic boundary conditions