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.

28 pages, 8 postscript figures