The present paper considers a finite spectrum assignment problem for retarded nonlinear systems. Using extensions of the Lie derivative and the Lie bracket for differential difference equations, we previously proposed a finite spectrum assignment procedure for a class of retarded nonlinear systems. In the present paper, we derive a necessary and sufficient condition for the solvability of a class of finite spectrum assignment problem for retarded nonlinear systems. The obtained condition is an extension of the condition for the exact linearization of finite dimensional nonlinear systems and the finite spectrum assignment of retarded linear systems with controllability over polynomial rings.