We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coe cients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differentialdifference equations, which has a unique generalized solution. It is proved that the smoothness of this solution can be violated on the considered interval and is preserved only on some subintervals. Su cient conditions for the initial function are obtained to ensure the smoothness of the generalized solution over the entire interval.