  We calculate the cross section and the transverse momentum distribution of
inclusive J/\psi production in \gamma \gamma collisions at CERN LEP2 within the
colour singlet model and the k_T-factorization approach, including both direct
and resolved photon contributions. The unintegrated gluon distribution in the
photon is determined, using the Blumlein's prescription for unintegrated gluon
distribution in a proton. We compare our theoretical predictions with
preliminary data taken by the DELPHI collaboration at LEP2. In addition, we
present our predictions for the J/\psi polarization properties.
