  In this paper we study inclusive production of vector charmonium states
$J/\psi$ or $\psi(2S)$ in two-photon $\epem$-annihilation at $\sqrt s=10.6 \rm
GeV$ using color-singlet model. Analytic expressions for differential cross
sections, numerical values of total cross sections and plots of different
distributions are presented. These distributions differ significantly from the
one-photon case so these modes can be easily separated.
