We study the helicity amplitudes of the process gamma gamma --> gamma gamma
at high energy, which in the standard and SUSY models first arise at the o
ne-loop order. In the standard model (Sn I), the diagrams involve W, charge
d-quark, and lepton loops, while in SUSY, we also have contributions from c
hargino-, charged-sfermion, and Higgs-loop diagrams. The SUSY contributions
are most important in the region above the threshold for producing the sup
ersymmetric partners; there, they interfere most effectively with the prima
rily imaginary SM amplitudes. Simple expressions for the relevant one-loop
functions are given which provide a direct overview of the behaviour of the
helicity amplitudes in the whole parameter space at high energies. The var
ious characteristics of a large set of observables are studied in detail.