  We present the full ${{\cal O}}(\alpha)$ electroweak radiative corrections to
single Higgs production in \epemt. This takes into account the full one-loop
corrections as well as the effects of hard photon radiation. We include both
the fusion and Higgs-strahlung processes. The computation is performed with the
help of {\tt GRACE-loop} where we have implemented a generalised non-linear
gauge fixing condition. The latter includes 5 gauge parameters that can be used
for checks on our results. Besides the UV, IR finiteness and gauge parameter
independence checks it proves also powerful to test our implementation of the
5-point function. We find that for a 500GeV machine and a light Higgs of mass
150GeV, the total ${{\cal O}}(\alpha)$ correction is small when the results are
expressed in terms of $\alpha_{{\rm QED}}$. The total correction decreases
slightly for higher energies. For moderate centre of mass energies the total
${{\cal O}}(\alpha)$ decreases as the Higgs mass increases, reaching -10% for
$M_H=350$GeV and $\sqrt{s}=500$GeV. In order to quantify the genuine weak
corrections we have subtracted the universal virtual and bremsstrahlung
correction from the full ${{\cal O}}(\alpha)$. We find, for $M_H=150$GeV, a
weak correction slowly decreasing from -2% to -4% as the energy increases from
$\sqrt{s}=300$GeV to $\sqrt{s}=1$TeV after expressing the tree-level results in
terms of $G_\mu$
