In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued...