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In the framework of the Brueckner-Bethe-Goldstone theory, we determine afully microscopic equation of state for asymmetric and $\beta$-stable nuclearmatter containing $\sim$ and $\la$ hyperons. We use the Paris and the newArgonne $Av_{18}$ two-body nucleon interaction, whereas the nucleon-hyperoninteraction is described by the Njimegen soft-core model. We stress the roleplayed by the three-body nucleon interaction, which produces a strong repulsionat high densities. This enhances enormously the hyperon population, andproduces a strong softening of the equation of state, which turns out almostindependent on the nucleon-nucleon interaction. We use the new equation ofstate in order to calculate the structure of static neutron stars. We obtain amaximum mass configuration with $M_{\rm max}$ = 1.26 (1.22) when the Paris($Av_{18}$) nucleon potential is adopted. Central densities are about 10 timesnormal nuclear matter density. Stellar rotations, treated within a perturbativeapproach, increase the value of the limiting mass by about 12%

Hyperon stars in the Brueckner-Bethe-Goldstone theory