  We discuss the theory of jet events in high-energy photon-proton interactions
using a model which gives a good description of the data available on total
inelastic $\gamma p$ cross sections up to $\sqrt{s}$=210 GeV. We show how to
calculate the jet cross sections and jet multiplicities and give predictions
for these quantities for energies appropriate for experiments at the HERA $ep$
collider and for very high energy cosmic ray observations.
