  We introduce a Renormalization scheme for the one and two dimensional
Forest-Fire models in order to characterize the nature of the critical state
and its scale invariant dynamics. We show the existence of a relevant scaling
field associated with a repulsive fixed point. This model is therefore critical
in the usual sense because the control parameter has to be tuned to its
critical value in order to get criticality. It turns out that this is not just
the condition for a time scale separation. The critical exponents are computed
analytically and we obtain $\nu=1.0$, $\tau=1.0$ and $\nu=0.65$, $\tau=1.16$
respectively for the one and two dimensional case, in very good agreement with
numerical simulations.
