Vanishing cycles of irregular D-modules

Considering a holonomic cal D-module and a hypersurface, we define a finite family of cal D-modules on the hypersurface which we call modules of vanis hing cycles. The first one had been previously defined and corresponds to f ormal solutions. The last one corresponds, via Riemann-Hilbert, to the geom etric vanishing cycles of Grothendieck-Deligne. For regular holonomic cal D -modules there is only one sheaf and for non regular modules the sheaves of vanishing cycles control the growth and the index of solutions. Our result s extend to non holonomic modules under some hypothesis.