  In this paper we study leading neutron production in photon - hadron
interactions which take place in $pp$ and $pA$ collisions at large impact
parameters. Using a model that describes the recent leading neutron data at
HERA, we consider exclusive vector meson production in association with a
leading neutron in $pp/pA$ collisions at RHIC and LHC energies. The total cross
sections and rapidity distributions of $\rho$, $\phi$ and $J/\Psi$ produced
together with a leading neutron are computed. Our results indicate that the
study of these processes is feasible and that it can be used to improve the
understanding of leading neutron processes and of exclusive vector meson
production.
