The optimal control of linear differential-difference systems of neutral type, with respect to quadratic performance criteria over an infinite time interval is treated. The linear differential-difference systems with delays in coordinates, derivatives, and control actions are considered. The Lyapunov-Bellman formalism is used to find the optimal solution. The global optimality of the solution follows from convexity of the set of admissible controls and of the cost functional, and linearity of the constraints. The computational procedure is based on considering the approximate optimal problem. A connection is established between the original and approximate optimal problems.