Abstract submitted to the International Europhysics Conference on High Energy Physics July 12 - 18, 2001, Budapest, Hungary _________________________________________________________________________ Exclusive photoproduction of J/psi mesons at HERA ZEUS Collaboration Abstract The exclusive photoproduction of J/psi mesons, gamma p -> J/psi p, has been studied in ep collisions using both the muon and electron decay channels with the ZEUS detector at HERA using integrated luminosities of 38 and 55 pb^{-1}, respectively. The spin-density matrix elements r^{04}_{00} and r^{04}_{1-1} have been measured from the decay-angle distributions and found to be consistent with expectations based on s-channel-helicity conservation. The total cross section has been measured as a function of the photon-proton centre-of-mass energy, W, in the kinematic range 20 < W < 290 GeV. The differential cross section, dsigma/dt, where t is the squared four-momentum transfer at the proton vertex, has also been measured for |t| < 1.5 GeV^2. The Pomeron trajectory has been determined.