This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation with nonlinear damping locally distributed u(tt) - Delta u + a(x) g(u(t)) = 0 in Omega x (0, infinity) subject to Dirichlet boundary conditions where Omega subset of R-n n >= 2 is an unbounded open set with finite measure and unbounded smooth boundary partial derivative Omega = Gamma. The function a(x), responsible for the localized effect of the dissipative mechanism, is assumed to be nonnegative and essentially bounded and, in addition, a (x) >= a(0) > 0 a. e. in omega, where omega = omega' boolean OR {x is an element of Omega; parallel to x parallel to| > R} (R > 0) and omega' is a neighborhood in Omega of the closure of partial derivative Omega boolean AND B-R, where B-R = {x is an element of Omega; parallel to x parallel to < R}.