In this paper we consider the nonlinear degenerate evolution equation with strong damping, (The equation is abbreviated) where K is a function with K(x, t) ≥ 0, K(x, 0) = 0 and F is a continuous real function satisfying (**) sF(s) ≥ 0, for all s ∈ R, Ω is a bounded domain of R^n, with smooth boundary Г. We prove the existence of a global weak solution for (*).