  We study at LEP II and Next Linear Collider energies Higgs production via the
bremsstrahlung channel $e^+e^-\ar ZH$, with $Z\ar \mu^+\mu^-$ and $H\ar b\bar
b$, and the corresponding irreducible background, in presence of hard photon
radiation, both from the initial and the final state. We carry out an analysis
that includes the computation of all the relevant contributions to the complete
tree--level matrix element for $e^+e^-\ar \mu^+\mu^- b\bar b\gamma $ and makes
use of the one at leading order $e^+e^-\ar \mu^+\mu^- b\bar b$ interfaced with
electron structure functions. We concentrate on the case of mass degeneracy
$M_H\approx M_Z$, for which next--to--leading electromagnetic contributions can
modify the content of $b\bar b$--pairs coming from $H$ and $Z$ decays. A brief
discussion concerning the case $M_H\not\approx M_Z$ is also given.
