  An interpretation of the Casselman-Wallach (C-W) Theorem is that the
$K$-finite functor is an isomorphism of categories from the category of
finitely generated, admissible smooth Fr\'echet modules of moderate growth to
the category of Harish-Chandra modules for a real reductive group, $G$ (here
$K$ is a maximal compact subgroup of G).In this paper we study the dependence
of this functor on parameters. Our main result implies that holomorphic
dependence implies holomorphic dependence. The work uses results from the
excellent thesis of van der Noort. Also a remarkable family of Universal
Harish-Chandra modules developed in this paper plays a key role.
