  The purpose of this paper is to give some generalizations, in the context of
Banach mani- folds, of Sussmann's results about the orbits of families of
vector fields ([Su]). Essentially, we define the notion of "l1-orbits" for any
family of vector fields on a Banach manifold, and we prove, under appropriate
assumptions, that such an orbit is a weak Banach submanifold.
