If $\Gamma$ is a discrete subgroup of $PSL(3,\Bbb{C})$, it is determined the
equicontinuity region $Eq(\Gamma)$ of the natural action of $\Gamma$ on
$\Bbb{P}^2_\Bbb{C}$. It is also proved that the action restricted to
$Eq(\Gamma)$ is discontinuous, and $Eq(\Gamma)$ agrees with the discontinuity
set in the sense of Kulkarni whenever the limit set of $\Gamma$ in the sense of
Kulkarni, $\Lambda(\Gamma)$, contains at least three lines in general position.
Under some additional hypothesis, it turns out to be the largest open set on
which $\Gamma$ acts discontinuously.