  The processes $\gamma\gamma\to\pi^0\pi^0\pi^0$ and $\gamma\gamma\to \pi^+
\pi^- \pi^0$ are considered in Generalized Chiral Perturbation theory, in view
of their potential sensitivity to the mechanism of spontaneous breaking of
chiral symmetry and to various counterterms. The amplitudes are computed up to
order ${\cal O}(p^6)$. The event production rates are estimated for the Daphne
$\phi$-Factory and for a future $\tau$-Charm Factory.
