We prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity ofthe type u″ - M(∫Ω ∇u 2dx)Δu+a(x)g(u′) + f(u) = 0, in Ω×]0,+∞[,u = 0, on Γ×]0,+∞[,u(x,0) = u0(x), u ′(x,0) = u1 (x), in Ω.