In general, retarded functional differential equations have an infinite dimensional character, in the sense that there exist an infinite number of linear independent characteristic solutions p j ( t) e λ j t , where λ j denotes a zero of a transcendental equation and p j a polynomial. In this paper we use Laplace transform methods to study the asymptotic behaviour of the solutions of this type of differential equations. Furthermore, we present necessary conditions such that a solution can be represented as a series of characteristic solutions. With these results we then can study the geometric structure of the strongly continuous semigroup T( t) associated with a retarded functional differential equation. The main result will be a characterization of the closure of the system of generalized eigenfunctions of the infinitesimal generator A of T( t).