  We present theoretical predictions for the transverse-momentum distribution
of J/psi mesons promptly produced in gamma gamma collisions within the
factorization formalism of nonrelativistic quantum chromodynamics, including
the contributions from both direct and resolved photons, and we perform a
conservative error analysis. The fraction of J/psi mesons from decays of
bottom-flavoured hadrons is estimated to be negligibly small. New data taken by
the DELPHI Collaboration at LEP2 nicely confirm these predictions, while they
disfavour those obtained within the traditional colour-singlet model.
