  We present the first calculation of QED radiative corrections to
deep-inelastic electron-photon scattering in terms of those variables that are
reconstructed in measurements of the photon structure function in
electron-positron collisions. In order to cover the low-$Q^2$ region, we do not
invoke the QCD-improved parton model but rather express our results in terms of
the photon structure functions. Both analytical and numerical results are
given.
