  In this paper we study the locus of generalized degree $d$ Henon maps in the
parameter space $\operatorname{Rat}_d^N$ of degree $d$ rational maps
$\mathbb{P}^N\to\mathbb{P}^N$ modulo the conjugation action of
$\operatorname{SL}_{N+1}$. We show that Henon maps are in the GIT unstable
locus if $N\ge3$ or $d\ge3$, and that they are semistable, but not stable, in
the remaining case of $N=d=2$. We also give a general classification of all
unstable maps in $\operatorname{Rat}_2^2$.
