  The nucleation process of quark matter in cold (T = 0) stellar matter is
investigated using the microscopic Brueckner-Hartree-Fock approach to describe
the hadronic phase, and the MIT bag model, the Nambu-Jona-Lasinio, and the
Chromo Dielectric models to describe the deconfined phase of quark matter. The
consequences of the nucleation process for neutron star physics are outlined.
Hyperonic stars are metastable only for some of the quark matter equations of
state considered. The effect of an hyperonic three body force on the
metastability of compact stars is estimated, and it is shown that, except for
the Nambu-Jona-Lasinio model and the MIT bag model with a large bag pressure,
the other models predict the formation of hybrid stars with a maximum mass not
larger than \sim 1.62 M\odot .
