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