We discuss the mechanism of dilepton production in proton-proton scattering via fusion of virtual
photons with identification of one proton on either side. This is relevant for the ATLAS+AFP
and CMS+PPS at the LHC. Transverse momenta of the photons are taken into account via photon
unintegrated fluxes. The latter ones are expressed in terms of proton electromagnetic form factors
and structure functions. We include different categories of such processes (double elastic, single
dissociative). Some differential distributions are shown explicitly and differences with respect to
the results without proton identification are discussed. A soft gap survival factor is calculated
using SuperChic-4 code.