  In this work we investigate the inclusive and exclusive photoproduction of
dileptons, which is relevant for the physics programme to be studied in the
proposed electron-proton collider, the LHeC. In the inclusive case, the process
is sensitive to the parton distribution functions in the photon whereas the
exclusive channel is connected to the small-$x$ QCD dynamics. For the latter,
we investigate the role played by saturation physics at a very high energy
scenario. The estimates for production cross sections and the number of events
are presented.
