In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fully microscopic equation of state for asymmetric and β-stable nuclear matter containing Σ and Λ hyperons. We use the Paris and the new Argonne Av18 two-body nucleon interaction, whereas the nucleon-hyperon interaction is described by the Njimegen soft-core model. We stress the role played by the three-body nucleon intera...