  We explore the potential of a future e^+ e^- collider in the 0.5 TeV
center-of-mass energy range to detect intermediate or heavy Higgs bosons in the
Standard Model. We first briefly assess the production cross sections and
update the decay branching fractions for a Higgs boson of intermediate mass,
with M_Z < m_H < 2M_W. We then study in detail the possibility of detecting a
heavy Higgs boson, with m_H > 2M_W, through the production of pairs of weak
bosons. We quantitatively analyze the sensitivity of the process e^+ e^- --> nu
nubar W^+ W^- (ZZ) to the presence of a heavy Higgs-boson resonance in the
Standard Model. We compare this signal to various backgrounds and to the
smaller signal from e^+ e^- --> ZH --> mu^+ mu^- W^+ W^- (ZZ), assuming the
weak-boson pairs to be detected and measured in their dominant hadronic decay
modes W^+ W^- (ZZ) --> 4jets. A related Higgs-boson signal in 6-jet final
states is also estimated. We show how the main backgrounds from e^+ e^- W^+ W^-
(ZZ), e nu WZ, and t tbar production can be reduced by suitable acceptance
cuts. Bremsstrahlung and typical beamstrahlung corrections are calculated.
These corrections reduce Higgs-boson production by scattering mechanisms but
increase production by annihilation mechanisms; they also smear out some
dynamical features such as Jacobian peaks in p_T(H). With all these corrections
included, we conclude that it should be possible to detect a heavy Higgs-boson
signal in the nu nubar W^+ W^-(ZZ) channels up to mass m_H=350 GeV.
