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The present paper is focused on the analysis on the existence of positive solutions of a second order differential system with two delays
\begin{equation} \left\{\begin{array}{lcr}x_{1}^{\prime\prime}(t)-a_{1}(t)x_{1}(t)+m_{1}(t)f_{1}(t,x(t),x_{\tau}(t))=0,\ \ t>0,\\ x_{2}^{\prime\prime}(t)-a_{2}(t)x_{2}(t)+m_{2}(t)f_{2}(t,x(t),x_{\tau}(t))=0,\ \ t>0,\\ x_{1}(t)=0,\ \ -\tau_{1}\ \leq t\leq 0,\;\mbox{and}\;\lim_{t\rightarrow\infty}x_{1}(t)=0,\\ x_{2}(t)=0,\ \ -\tau_{2}\ \leq t\leq 0,\;\mbox{and}\;\lim_{t\rightarrow\infty}x_{2}(t)=0\end{array}\right.\nonumber \\ \end{equation}by using two well-known fixed point theorems.
