[en] We present a complete calculation of the higher-order perturbative QCD corrections to inelastic photoproduction of J/ψ particles. A comprehensive analysis of total cross sections and differential distributions for the energy range of the fixed-target experiments and for inelastic J/ψ photoproduction at HERA is performed. The cross section and the J/ψ energy spectrum are compared with the available photoproduction data incliding first results from HERA. This analysis will not only provide information on the gluon distribution of the proton but appears to be a clean test for the underlying picture of quarkonium production as developed so far in the perturbative QCD sector. (orig.)