Inelastic photoproduction of J/Psi particles at high energies is one o
f the processes to determine the gluon distribution in the nucleon. We
have calculated the QCD radiative corrections to the color-singlet mo
del of this reaction. They are large at moderate photon energies, but
decrease with increasing energies. The cross section and the J/Psi ene
rgy spectrum are compared with the available fixed-target photoproduct
ion data and predictions are given for the HERA energy range.