  Consider the ring of holomorphic function germs in $C^n$ and denote by $M$
the maximal ideal of this ring. For any a holomorphic function germ $f$ with an
isolated critical point, the finite determinacy theorem (Mather-Tougeron)
asserts that there exists some $k$, such that $f+g$ can be brought back to $f$,
via a holomorphic change of variables, for any $g \in M^k$. In this paper, a
generalisation of this theorem for functions defined in a neighbourhood of a
Stein compact subset and for an arbitrary ideal is given.
