  We study the equation of state of hyperon-rich matter for neutron stars using
an extended relativistic mean-field model. We take special care of the recently
proposed non-linear behaviour of the vector field which gives a much better
description of Dirac-Brueckner calculations. The hyperon-hyperon interaction is
also implemented by introducing additional meson exchanges. These new terms
avoid the instability found at high densitites in previous works while keeping
the excellent description for finite nuclear systems. We also demonstrate
within the mean-field approach that the presence of hyperons inside neutron
stars on one hand and the hyperon-hyperon interactions on the other hand make
the onset of kaon condensation less favourable.
