  Measurements are reported of the production of dijet events with a leading
neutron in ep interactions at HERA. Differential cross sections for
photoproduction and deep inelastic scattering are presented as a function of
several kinematic variables. Leading order QCD simulation programs are compared
with the measurements. Models in which the real or virtual photon interacts
with a parton of an exchanged pion are able to describe the data.
Next-to-leading order perturbative QCD calculations based on pion exchange are
found to be in good agreement with the measured cross sections. The fraction of
leading neutron dijet events with respect to all dijet events is also
determined. The dijet events with a leading neutron have a lower fraction of
resolved photon processes than do the inclusive dijet data.
