[en] We have calculated the leading color-octet contributions to the production of J/ψ particles in photon-proton collisions. Using the values for the color-octet matrix elements extracted from fits to prompt J/ψ data at the Tevatron, we demonstrate that distinctive color-octet signatures should be visible in J/ψ photoproduction. However, these predictions appear at variance with recent experimental data obtained at HERA, indicating that the phenomenological importance of the color-octet contributions is smaller than expected from theoretical considerations and suggested by the Tevatron fits. (orig.)