Multiple Hard Interactions in Gamma-Gamma and Gamma-P Physics at LEP and HERA

At $e^+e^-$ and $ep$ colliders, the large fluxes of almost on-shell photons accompanying the lepton beams lead to the photoproduction of jets. As the centre-of-mass energy is increased, regions of smaller $x$ in the parton densities are explored and these are regions of high parton density. As a result, the probability for more than one hard partonic scattering occurring in a single $\gamma \gamma$ or $\gamma p$ collision can become significant. This effect has been simulated using an eikonal prescription combined with the HERWIG Monte Carlo program. The possible effects of multiple hard interactions on event shapes and jet cross sections have been studied in this framework at a range of energies relevant to HERA and LEPII. The results indicate that the effects could be significant.