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In this paper we consider a one dimensional elastic system with doubleporosity structure and with frictional damping in both porous equations. Weintroduce two stability numbers $\chi_{0}$ and $\chi_{1}$ and prove that thesolution of the system decays exponentially provided that $\chi_{0}=0$ and$\chi_{1}\neq0.$ Otherwise, we prove the lack of exponential decay. Our resultsimprove the results of \cite{Bazarra} and \cite{Nemsi}.

On the stability of a double porous elastic system with visco-porous dampings