In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fu
lly microscopic equation of state for asymmetric and beta-stable nuclear ma
tter containing Sigma(-) and Lambda hyperons. We use the Paris and the new
Argonne Au-18 two-body nucleon interaction, whereas the nucleon-hyperon int
eraction is described by the Njimegen soft-core model. We stress the role p
layed by the three-body nucleon interaction, which produces a strong repuls
ion at high densities. This enhances enormously the hyperon population, and
produces a strong softening of the equation of state, which turns out almo
st independent on the nucleon-nucleon interaction. We use the new equation
of state in order to calculate the structure of static neutron stars. We ob
tain a maximum mass configuration with M-max = 1.26 (1.22) when the Paris (
Au-18) nucleon potential is adopted. Central densities are about 10 times n
ormal nuclear matter density. Stellar rotations, treated within a perturbat
ive approach, increase the value of the limiting mass by about 12%.