Sur la topologie d'une famille de pinceaux de germes d'hypersurfaces complexes

We study the pencils of germs of complex hypersurfaces defined by the couples (ƒ, g): (C^{n+1, 0}) → (C², 0) without blowing-up in codimension 0. We approximate the equisingularity set of such a pencil in terms of the tangent directions to the discriminant germ of the morphism (ƒ, g). We next compare the monodromy modules of the generic member of this pencil with those of the atypical ones.