In this paper we consider the nonlinear degenerate evolution equation with strong damping, ( * )             { K ( x , t ) u t t − Δ u − Δ u t + F ( u ) = 0       in       Q = Ω × ] 0 , T [ u ( x , 0 ) = u 0 ,       ( k u ′ ) ( x , 0 ) = 0       in       Ω u ( x , t ) = 0                       on       ∑ = Γ × ] 0 , T [ where K is a function with K ( x , t ) ≥ 0 , K ( x , 0 ) = 0 and F is a continuous real function satisfying ( * * )           s F ( s ) ≥ 0 ,       for       all       s ∈ R ,                           Ω is a bounded domain of R n , with smooth boundary Γ . We prove the existence of a global weak solution for (*).