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We study at LEP II and Next Linear Collider energies Higgs production via thebremsstrahlung channel $e^+e^-\ar ZH$, with $Z\ar \mu^+\mu^-$ and $H\ar b\barb$, and the corresponding irreducible background, in presence of hard photonradiation, both from the initial and the final state. We carry out an analysisthat includes the computation of all the relevant contributions to the completetree--level matrix element for $e^+e^-\ar \mu^+\mu^- b\bar b\gamma $ and makesuse of the one at leading order $e^+e^-\ar \mu^+\mu^- b\bar b$ interfaced withelectron structure functions. We concentrate on the case of mass degeneracy$M_H\approx M_Z$, for which next--to--leading electromagnetic contributions canmodify the content of $b\bar b$--pairs coming from $H$ and $Z$ decays. A briefdiscussion concerning the case $M_H\not\approx M_Z$ is also given.Comment: ISR added, main conclusions unchanged (to be published in J. Phys. G

Standard model Higgs boson production and hard photon radiation in events at LEP II and the Next Linear Collider