We analyze the uniform general decay of the solution of a system modeling a mixture of two interacting continua with nonlinear localized damping acting in a arbitrary small region of the interval under consideration, assuming appropriate assumptions on the nonlinear terms. To do this, we used a observability inequality obtained for the conservative system combined with the Holmgren's uniqueness theorem and the reduction principle (see \cite{Daloutli}) where the problem of decay rates with nonlinear damping is reduced to an appropriate stabilizability inequality for the linear equation. This study generalizes and improves previous literature outcomes.