The process gamma --> ZH first arises at the one loop level, and as such it
provides us with remarkable tests of the structure of the electro-weak Hig
gs sector. These tests are complementary to those in the gauge sector invol
ving gamma gamma --> gamma, gammaZ, ZZ. We show that in the standard model
(SM) where H = H-SM, as well as in the supersymmetric ease where H = h(0),
H-0 or A(0), observables exist (like e.g. the energy dependence, angular di
stribution, photon polarization dependence or final Z polarization) which p
resent rather spectacular properties. Such properties involve strong thresh
old effects with steps, bumps or peaks, reflecting the type of Higgs and he
avy quarks and chargino masses and couplings predicted by the SM and supers
ymmetric models.