  First order QCD and leading QED corrections to Higgs boson production in the
channel $e^-p \to \nu H^0 X; H^0 \to b\bar{b}$ are calculated for the
kinematical conditions at LEP $\otimes$ LHC ($\sqrt{s} = 1360 \GeV$) and the
interesting mass range $80 < M_H < 150 \GeV$. In the DIS scheme the QCD
corrections (not including the corrections to the branching ratio, which are
well-known) are found to be about 1\% for the total cross section and $-13\%$
to $-10\%$ for the observable cross section as defined by appropriate cuts. The
latter results depend on the definition of these cuts. The QED corrections
amount to about $-5\%$. Also obtainable with anonymous ftp from
gluon.hep.physik.uni-muenchen.de.
