  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.
