In this section, we restrict our attention to the linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{t}},{\rm{x}}_{\rm{t}} } \right)$$ (17.1) where L(t,ϕ) is continuous in t,ϕ, linear in ϕ and is given explicitly by $${\rm{L}}\left( {{\rm{t}},{\rm{\phi }}} \right) = \sum\limits_{{\rm{k}} = 1}^\infty {{\rm{A}}_{\rm{k}} \left( {\rm{t}} \right){\rm{\phi }}\left( { - \tau _{\rm{k}} } \right) + } \int_{ - \tau }^0 {{\rm{A}}\left( {{\rm{t}},{\rm{\xi }}} \right)} {\rm{\phi }}\left( {\rm{\xi }} \right){\rm{d\xi }}$$ (17.2) where each Ak(t), A(t,ξ) are continuous n × n matrix functions for \(- \infty < t,\xi < \infty ,{\text{0}} \leqslant {{\tau }_{k}},\tau \leqslant r\). The extension of the results of this section to the most general linear system is contained in Section 32.