  The distribution of hadrons produced in deeply inelastic electron-proton
collisions depends on the azimuthal angle between lepton scattering plane and
hadron production plane in the photon-proton centre-of-mass frame. In addition
to the well known up-down asymmetry induced by the azimuthal dependence of the
Born level subprocess, there is also a non-vanishing left-right asymmetry,
provided the incoming electron is polarized. This asymmetry is
time-reversal-odd and induced by absorptive corrections to the Born level
process. We investigate the numerical magnitude of azimuthal asymmetries in
semi-inclusive hadron production at HERA with particular emphasis on a possible
determination of the time-reversal-odd asymmetry.
