  Using the CLEO-II detector at the CESR $e^+e^-$ storage ring running at the
center-of-mass energy around 10.6 GeV, we have studied exclusive production of
charmonium states in two-photon collisions. Employing a dataset comprising 3.0
${\rm fb}^{-1}$ we have searched for decays of the $\eta_c$, $\chi_{c0}$ and
$\chi_{c2}$ mesons resulting in four charged hadrons. We report on the
measurements of the cross sections and two-photon widths of these charmonium
states.
