  We calculate the universal radiative QED corrections to polarized lepton
scattering for general scattering cross sections in analytic form. The flavor
non--singlet and singlet radiation functions are calculated to $O((\alpha {\rm
L})^5)$. The resummation of the non--singlet and singlet contributions to the
QED--anomalous dimensions $\propto(\alpha \ln^2(x))^k$ is performed to all
orders. Numerical results are presented for the individual radiation functions.
Applications to polarized deeply inelastic lepton--nucleon scattering are
given.
