Summary.

We prove the following two results 1. For a proper holomorphic function f: X → D of a complex manifold X on a disc such that {df = 0} ⊂ f−1(0), we construct, in a functorial way, for each integer p, a geometric (a,b)-module Ep associated to the (filtered) Gauss-Manin connexion of f. This first theorem is an existence/finiteness result which shows that geometric (a,b)-modules may be used in global situations. 2. For any regular (a,b)-module E we give an integer N(E), explicitely given from simple invariants of E, such that the isomorphism class of E bN(E).E determines the isomorphism class of E. This second result allows to cut asymptotic expansions (in powers of b) o