  This article is the continuation of [B. 13-b] where we show how the
isomorphism class of a $[\lambda]-$primitive theme with a given Bernstein
polynomial may be characterized by a (small) finite number of complex
parameters. We construct here a corresponding locally versal holomorphic
deformation of $ [\lambda]-$primitive themes for each given Bernstein
polynomial. Then we prove the universality of the corresponding "canonical
family" in many cases. We also give some examples where no local universal
family exists.
