  Consider a pseudogroup on (C,0) generated by two local diffeomorphisms having
analytic conjugacy classes a priori fixed in Diff(C,0). We show that a generic
pseudogroup as above is such that every point has (possibly trivial) cyclic
stabilizer. It also follows that these generic groups possess infinitely many
hyperbolic orbits. This result possesses several applications to the topology
of leaves of foliations and we shall explicitly describe the case of nilpotent
foliations associated to Arnold's singularities of type A^{2n+1}.
