Abstract submitted to the XXXth International Conference on High Energy Physics July 27 - August 2, 2000, Osaka, Japan _________________________________________________________________________ Study of exclusive photoproduction of J/psi mesons in ep interactions at HERA ZEUS Collaboration Abstract Exclusive photoproduction of J/psi mesons, gamma p --> J/psi p, has been measured in ep collisions with the ZEUS detector at HERA using an integrated luminosity of 36 pb-1. The dependence of the cross section on the photon-proton centre of mass energy, W, is presented as well as the W dependence of the J/psi transverse momentum distributions with respect to the photon direction. The Pomeron trajectory is determined.