Two local existence results are obtained for strongly nonlinear functional differential equations of the form \(du/dt(t)+Au(t)\ni F(t,u_ t),\) \(0\leq t\leq T\), \(u(s)=g(s)\), -r\(\leq s\leq 0\). With X a real Banach space, A: D(A)\(\subset X\to 2\) X a m-accretive operator, possibly nonlinear and multivalued, U a nonempty subset in C([-r,0];X), F: [0,T]\(\times U\to X\) is a given mapping and \(g\in U\) satisfies g(0)\(\in D(A)\). The results require certain compactness properties on the operator A. Examples illustrate the applicability of the theory.