Nonlinear perturbations of linear Volterra integral equations are studied in an abstract setting which contains and generalizes some earlier results on the same problem. The perturbed problem is first written as a variation of constants equation on a Fréchet space. It is then shown that standard fixed point theorems may be applied if the linear equation is admissible w.r.t. a Banach subspace of the Fréchet space. This theory is applied to an example where L 2 {L^2} -stability is proved.