The decay K-L --> pi(0)<nu(nu)over bar> is an excellent probe of the n
ature of CP violation. It is almost entirely CP violating, and hadroni
c uncertainties are negligible. Experiments which hope to detect the d
ecay are currently being planned. We calculate the decay rate in sever
al extensions of the standard model Higgs sector, including the Liu-Wo
lfenstein two-doubler model of spontaneous CP violation and the Weinbe
rg three-doublet model. in a model with an extra doublet, with CP viol
ation arising from the CKM sector, the rate can increase by up to 50%.
However, in models in which the CP violation arises either entirely o
r predominantly from the Higgs sector. we find that the decay rate is
much smaller than that of the standard model, unless parameters of the
model are fine-tuned.