  The joint effect of the density dependence of the symmetry energy and
strangeness content on the structure of cold neutron stars is studied within
the framework of a relativistic mean field theory. It is shown that 2$M_\odot$
are obtained for repulsive $YY$ interaction and preferably for a small or a
large slope $L$. An attractive $\Sigma$ potential in nuclear matter will favor
the appearance of strangeness in stars with a mass as small as $\sim 1
M_\odot$, if, however it is repulsive only stars with a mass $\gtrsim 1.4
M_\odot$ will contain strangeness. The joint effect of reducing the symmetry
energy slope and including hyperons is to farther reduce the radius. Neutron
star maximum mass evolve non-monotonically with the symmetry energy slope, and
the smallest masses are obtained for values $L\sim 80$ MeV. Other neutron star
variables evolve nonlinearly with the slope of the symmetry energy and depend
on the hyperon-nucleon and hyperon-hyperon couplings. The radius of a neutron
star is linearly correlated with the neutron star total strangeness fraction
and the slope is independent of the slope of the symmetry energy and the mass
of the star.
