Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2031 2023 2023 College Of Pharmacy, AL-Farahidi University, Baghdad, Iraq Murtada Ali Maqdisi We study under some conditions on p, m and suitable conditions on g, the decay of solutions of the nonlinear viscoelastic hyperbolic equation in problem (P) as t→+∞, with Ω is a bounded domain in R^N (N>1), with smooth boundary Γ, and a, b, w are positive constants, m≥2, P≥2, and the function g(t) satisfying some conditions. We show that the energy of solutions decays exponentially if m =2 and polynomial if m >2, provided that the initial data are small enough. 2023 2023 47 55 10.54216/PMTCS.010104 https://www.americaspg.com/articleinfo/40/show/2031