Sufficient conditions are established for the oscillation of proper solutions of the system $$\begin{array}{cc}\hfill u_1^{\text{'}}\left(t\right)& =p\left(t\right)u_2\left(\sigma \left(t\right)\right),\hfill \\ \hfill u_2^{\text{'}}\left(t\right)& =-q\left(t\right)u_1\left(\tau \left(t\right)\right),\hfill \end{array}$$ where $p,q:R_{+}\to R_{+}$ are locally summable functions, while $\tau$ and $\sigma :R_{+}\to R_{+}$ are continuous and continuously differentiable functions, respectively, and $\underset{t\to +\infty }{lim}\tau \left(t\right)=+\infty$, $\underset{t\to +\infty }{lim}\sigma \left(t\right)=+\infty$.