If the standard model (SM) Higgs particle is sufficiently heavy, then its c
ontribution to gamma gamma --> ZZ should be largely imaginary, interfering
with the also predominantly imaginary SM "background" generated by the W lo
op. For standard model Higgs masses in the region 200 less than or similar
to m(H) less than or similar to 500 GeV, this interference is found to be c
onstructive and increasing the Higgs signal. In the minimal SUSY case an in
terference effect should also appear for the contribution of the heavier CP
-even neutral Higgs boson H-0, provided it is sufficiently heavy. The effec
t is somewhat reduced, though, by the smallness of the H-0 width and the ga
mma gamma and ZZ branching ratios. The interference is again found to be co
nstructive for part of the parameter space corresponding to sfermion masses
at the TeV scale and maximal stop mixing. For both the SM and the SUSY cas
e, regions of the parameter space exist, though, where the interference may
be destructive. It is therefore essential to take these effects into accou
nt when searching for possible scalar Higgs-like candidates. To this aim, w
e present the complete analytic expressions for both resonance and backgrou
nd amplitudes.