  We consider the possibility of detecting a heavy Higgs boson ($m_H>2m_Z$) in
proposed $\gamma\gamma$ colliders through the semi-leptonic mode $\gamma\gamma
\rightarrow H \rightarrow ZZ \rightarrow q\bar q \ell^+\ell^-$. We show that
due to the non-monochromatic nature of the photon beams produced by the
laser-backscattering method, the resultant cross section for Higgs production
is much smaller than the on-resonance cross section and generally {\it
decreases} with increasing collider energy. Although continuum $ZZ$ production
is expected to be negligible, we demonstrate the presence of and calculate
sizeable backgrounds from $\gamma\gamma\rightarrow \ell^+\ell^-Z,\,q\bar qZ$,
with $Z\rightarrow q\bar q,\,\ell^+\ell^-$, respectively, and
$\gamma\gamma\rightarrow t\bar t\rightarrow b\bar b\ell^+\ell^-\nu\bar\nu$.
This channel may be used to detect a Higgs of mass $m_H$ up to around 350~GeV
at a 0.5~TeV $e^+e^-$ collider, assuming a nominal yearly luminosity of
10--20~fb$^{-1}$.
