Measurement of inelastic J/psi helicity distributions with ZEUS at HERA The decay angular distributions of inelastic photoproduction of J/psi mesons were measured with the ZEUS detector at HERA, using an integrated luminosity of 470 pb-1. J/psi mesons were identied using the decay mode J/psi -> mu+ mu- and were measured in the range 50 < W < 180 GeV, where W is the photon proton centre-of-mass energy. The polar and azimuthal distributions of the mu+ in the J/psi rest frame are presented as a function of pT , for pT > 1 GeV and z > 0.4, and as function of z, for pt > 1 GeV and 0.1 < z < 0.9, where pT is the transverse momentum of the J/psi in the laboratory frame and z is the fraction of the incident photon energy carried by the J/psi in the proton rest frame. The experimental results are compared to the theoretical predictions at leading order.