In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local α -condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.