New fixed point theorems for multivalued maps between Fr�chet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Fr�chet space as the projective limit of a sequence of Banach spaces. In particular we use degree and index theory and a Lefschetz fixed point theorem to obtain applicable fixed point theorems in Fr�chet spaces for general classes of maps.

fixed point theory, Volterra operators, projective limits.