  The classical Julia-Wolff-Caratheodory Theorem is one of the main tools to
study the boundary behavior of holomorphic self-maps of the unit disc of $\C$.
In this paper we prove a Julia-Wolff-Caratheodory's type theorem in the case of
the polydisc of $\C^n.$ The Busemann functions are used to define a class of
"generalized horospheres" for the polydisc and to extend the notion of
non-tangential limit. With these new tools we give a generalization of the
classical Julia's Lemma and of the Lindelof Theorem, which the new
Julia-Wolff-Caratheodory Theorem relies upon.
