  Meson--photon--photon transition form factors for S-, P-, and D-wave states
are calculated, the meson being treated as a non-relativistic
heavy-quark--antiquark pair. The full dependence on both photon virtualities is
included. Cross-section formulas for charge-conjugation even mesons with J^P =
0^-, 0^+, 1^+, 2^+, and 2^- in electron--positron collisions are presented and
numerical results for LEP energies are given. In particular, we find two-photon
event rates for \chi_{\rc 1}, \eta_{\rc}(2S), and \eta_{\rb}(1S) within reach
of LEP.
  With minor modifications to incorporate SU(3)-flavour breaking we estimate
rates for 18 light mesons as well, based on the observation that their
two-photon decay widths agree remarkably well with measured data. Finally we
point out that e^+ e^- cross sections for 1^+ states do not vanish at low Q^2,
the Landau--Yang suppression factors of the two-photon cross sections being
compensated by the photon propagators.
