  At HERA, the large flux of almost real photons accompanying the electron beam
leads to the copious photoproduction of jets. Regions of small momentum
fractions $x$ of the incoming particles are explored, where the density of
partons is high. As a result, the probability for more than one hard partonic
scattering occurring in a single $\gamma p$ collision could become significant.
It is well known that this effect modifies the contribution of jets (minijets)
to the total cross section. We discuss the latest HERA data on the total
$\gamma p$ cross section in this context. The possible effects of multiple hard
interactions on event shapes and jet cross sections at HERA have been studied
using Monte Carlo programs. We review some of the available results, which in
general indicate that the effects of multiple interactions should be
significant and may already be manifest in the existing HERA data.
