We consider the problem of applying the averaging method to the asymptotic approximation of solutions of functional-differential equations of neutral type $\dot{x}(t)\in\varepsilon F(t,x(t),\dot{x}(t))$ in the case where the average of the right-hand side does not exist. Our paper generalizes results of W. A. Plotnikow, W. M. Sawczenko from [8] where the generalized system $\dot{x}(t)\in\varepsilon F(t,x)$ was investigated.