  The leptonic QED radiative corrections are calculated in the next-to-leading
log approximation ${\cal O}[\alpha^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply
inelastic $ep$--scattering in the case of mixed variables. The corrections are
determined using mass factorization in the OMS--scheme for the
double--differential scattering cross sections.
