  A next-to-leading order QCD calculation for single-inclusive jet
photoproduction in unpolarized and longitudinally polarized lepton-hadron
collisions is presented which consistently includes ``direct'' and ``resolved''
photon contributions. The computation is performed within the ``small-cone
approximation'' in a largely analytical form. Phenomenological aspects of jet
production at future ep colliders such as the CERN-LHeC and the polarized
BNL-eRHIC are discussed, placing particular emphasis on the perturbative
stability of the predictions and the possibility to constrain the parton
content of the photon.
