  The cross sections for inelastic photoproduction of J/psi and psi^prime
mesons have been measured in ep collisions with the ZEUS detector at HERA,
using an integrated luminosity of 468 pb-1 collected in the period 1996--2007.
The psi^prime to J/psi cross section ratio was measured in the range 0.55 < z <
0.9 and 60 < W < 190 GeV as a function of W, z and p_T. Here W denotes the
photon-proton centre-of-mass energy, z is the fraction of the incident photon
energy carried by the meson and p_T is the transverse momentum of the meson
with respect to the beam axis. The J/psi cross sections were measured for 0.1 <
z < 0.9, 60 < W < 240 GeV and p_T > 1 GeV. Theoretical predictions within the
non-relativistic QCD framework including NLO colour--singlet and colour--octet
contributions were compared to the data, as were predictions based on the
k_T--factorisation approach.
