The authors study the nonlinear equation (1) \(\dot x = \varphi (y) - F(x)\), \(\dot y = - g(x)\), where \(F(x) = \int^x_0 t(\xi) d \xi\). They discuss the oscillation of the solutions of (1) and prove that the solution of the Cauchy problem for (1) is unique. Necessary and sufficient conditions for the oscillation of (1) are given.