  We prove an analogue for Stokes torsors of Deligne's skeleton conjecture and
deduce from it the representability of the functor of relative Stokes torsors
by an affine scheme of finite type over C. This provides, in characteristic 0,
a local analogue of the existence of a coarse moduli for skeletons with bounded
ramification, due to Deligne. As an application, we use the geometry of this
moduli to derive quite strong finiteness results for integrable systems of
differential equations in several variables which did not have any analogue in
one variable.
