  In the framework of the non-relativistic Brueckner-Bethe-Goldstone theory, we
derive a microscopic equation of state for asymmetric and $\beta$-stable matter
containing $\Sigma^-$ and $\Lambda$ hyperons. We mainly study the effects of
three-body forces (TBFs) among nucleons on the hyperon formation and the
equation of state (EoS). We find that, when TBFs are included, the stellar core
is almost equally populated by nucleons and hyperons. The resulting EoS, which
turns out to be extremely soft, has been used in order to calculate the static
structure of neutron stars. We obtain a value of the maximum mass of 1.26 solar
masses (1 solar mass $M_o \simeq 1.99 \cdot 10^{33} g$). Stellar rotations
increase this value by about 12%.
