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This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping?? u?? u =|u| u in? ×(0,+?)? tt???? u=0 on? ×(0,+?) 0 (1. 1)?? u+g(u)=0 on? ×(0,+?)? t 1???? 0 1 u(x,0) = u (x); u (x,0) = u (x),x??, t n where? is a bounded domain of R,n? 1, with a smooth boundary? =???. 0 1 Here,? and? are closed and disjoint and? represents the unit outward normal 0 1 to?. Problems like (1. 1), more precisely,? u?? u =?f (u)in? ×(0,+?)? tt 0???? u=0 on? ×(0,+?) 0 (1. 2)?? u =?g(u )?f (u)on? ×(0,+?)? t 1 1???? 0 1 u(x,0) = u (x); u (x,0) = u (x),x??, t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.