This chapter is dedicated to the case of neutral type linear systems with distributed delay. The structure of quadratic functionals that have prescribed time derivatives along the solutions of such a system is defined, and the corresponding Lyapunov matrices are introduced. A system of matrix equations that defines Lyapunov matrices is given. It is proven that under some conditions this system admits a unique solution. A general class of system with distributed delay for which Lyapunov matrices are solutions of special standard boundary value problems for an auxiliary system of linear matrix ordinary differential equations is presented. Complete type functionals are defined. It is shown that these functionals can be presented in a special form that is more convenient for the computation of lower and upper bounds for the functionals.