The author presents a discussion on the Carathéodory and Kobayashi pseudo-distances in the setting of complex analytic Banach manifolds over complex Banach spaces. The main known results on these two pseudo- distances in the classical setting of finite-dimensional complex analytic manifolds extend, in a natural way, to this analytic Banach manifolds setting. This extention is based on purely topological methods which are built in the very definition of these pseudo-distances. No discussion is given concerning the differential forms of these pseudo-distances.