The linear autonomous, neutral system of functional differential equations (*) \((d/dt)(\mu^*x(t)+f(t))=\nu *x(t)+g(t)\) (\(t\geq 0)\), \(x(t)=\phi (t)\) (\(t\leq 0)\), in a fading memory space is studied. Here \(\mu\) and \(\nu\) are matrix-valued measures supported on [0,\(\infty)\), finite with respect to a weight function, and f,g, and \(\phi\) are \(c^ n\)-valued, continuous or locally integrable functions, bounded with respect to a fading memory norm. Conditions which imply that solutions of (*) can be decomposed into a stable part and an unstable part are given. These conditions are of frequency domain type. The usual assumption that the singular part of u vanishes is not needed. The results can be used to decompose the semigroup generated by (*) into a stable part and an unstable part.