The present paper is focused on the analysis on the existence of positive solutions of a second order differential system with two delays \left \{{lcr} x_1''(t)-a_1(t)x_1(t)+m_1(t)f_1(t,x(t),x_\tau(t))=0,\ \ t>0,\\ x_2''(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,\;\; x_1(t)=0,\\ x_2(t)=0,\ \ -\tau_2\ \leq t \leq 0,\;\; x_2(t)=0 \right. by using two well-known fixed point theorems.