  We study Higgs boson production in association with a pair of electroweak
vector bosons ($WW,ZZ,Z\gamma$) at future $\epem$ colliders in the framework of
the Standard Model. Total cross sections and distributions for the
intermediate-mass Higgs are presented, with special emphasis on the Next Linear
Collider (NLC) case operating at a centre-of-mass energy $\sqrt{s} \simeq 500$
GeV, where the cross sections turn out to be more favourable than in
larger-$\sqrt{s}$ collisions. We find that with an integrated luminosity of 20
fb$^{-1}$ there is a sizeable event rate for the $HWW$ and $HZ\gamma$ (with a
high $p_T^{\gamma}$) channels, while a larger integrated luminosity is needed
to study the $HZZ$ production. We take into account various backgrounds,
notably top-pair and triple vector-boson production, and show ways to
significantly reduce their effects.
