  We introduce a variant of the usual Kahler forms on free and almost free
divisors and their deformations, and show that they enjoy the same depth
properties as Kahler forms on isolated complete intersection singularities.
Using these forms, it is possible to describe analytically the vanishing
cohomology in families of free divisors, in precise analogy with the classical
description for the Milnor fibration of an ICIS, due to Brieskorn and Greuel.
This applies in par- ticular to the family of discriminants of a versal
deformation of an unstable map-germ.
