  The inelastic production of J/psi mesons in e p collisions has been studied
with the ZEUS detector at HERA using an integrated luminosity of 109 pb-1. The
J/psi mesons were identified using the decay channel J/psi -> mu+ mu-. The
measurements were performed in the kinematic range 2 < Q^2< 80 Gev^2, 50 < W <
250 Gev, 0.2 < z <0.9 and -1.6 < Ylab < 1.3, where Q^2 is the virtuality of the
exchanged photon, W is the photon-proton centre-of-mass energy, z is the
fraction of the photon energy carried by the J/psi meson in the proton rest
frame and Ylab is the rapidity of the J/psi in the laboratory frame. The
measured cross sections are compared to theoretical predictions within the
non-relativistic QCD framework including colour-singlet and colour-octet
contributions, as well as to predictions based on the kT-factorisation
approach. Calculations of the colour-singlet process generally agree with the
data, whereas inclusion of colour-octet terms spoils this agreement.
