  The H1 Collaboration at the DESY electron-proton collider HERA has observed,
in photoproduction and neutral-current deep-inelastic scattering, an unexpected
excess of events with isolated leptons and missing transverse momentum,
especially at large values of hadronic transverse momentum - a signature
typical for single top-quark production. This observation is being
substantiated in the HERA II run. Motivated by this, we evaluate the cross
section of single top-quark photo- and electroproduction both in the standard
model and its minimal supersymmetric extension, considering both minimal and
non-minimal flavour-violation scenarios in the latter case.
