  Let F be a germ of a singular foliation of the complex plane. Assuming that F
is a generalized curve D. Marin and J.-F. Mattei proved the incompressibility
of the foliation in a neighborhood from which a finite set of analytic curves
is removed. We show in the present work that this hypothesis cannot be eluded
by building examples of foliations, reduced after one blow-up, for which the
property does not hold. Even if we manage to prove that the individual
saddle-node foliation is incompressible, their leaves not retracting
tangentially on the boundary of the domain of definition forbids a
generalization of Marin--Mattei's construction. We finally characterize those
foliations for which the construction of Marin--Mattei's monodromy can be
carried out.
