  We consider the problem of interpolating a holomorphic family of
nondegenerate holomorphic jets on C^n for n > 1, parametrized by points in a
Stein manifold, by a holomorphic family of automorphisms of C^n. We show that
under a suitable topological condition it is possible to find a solution,
thereby generalizing results of Forstneric and Varolin concerning the
nonparametric jet interpolation by automorphisms.
