  In this talk we discuss the predictions of local realistic theories for the
evolution of a K0-K0bar quantum entangled pair created in the decay of the
phi-meson. It is shown, in agreement with Bell's theorem, that the most general
local hidden-variable model fails in reproducing the whole set of
quantum-mechanical observables. We achieve this conclusion by employing two
different approaches. In the first approach, the local realistic observables
are deduced from the most general premises concerning locality and realism, and
Bell-like inequalities are not employed. The other approach makes use of Bell's
inequalities. Under particular conditions for the detection times, within the
first approach the discrepancy between quantum mechanics and local realism for
the asymmetry parameter turns out to be not less than 20%. A similar
incompatibility can be made evident by means of a Bell-type test, by employing
a Clauser-Horne-Shimony-Holt's inequality written in terms of properly
normalized observables. Because of its relatively low experimental accuracy,
the data obtained by the CPLEAR collaboration do not yet allow a decisive test
of local realism. Such a test, both with and without the use of Bell's
inequalities, should be feasible in the future at the Frascati Phi-factory.
