  We try to single out some qualitative new effects of the coupling to the
$\delta$-isovector-scalar meson introduced in a minimal way in a
phenomenological hadronic field theory. Results for the equation of state
($EOS$) and the phase diagram of asymmetric nuclear matter ($ANM$) are
discussed. We stress the consistency of the $\delta$-coupling introduction in a
relativistic approach. New contributions to the slope and curvature of the
symmetry energy and the neutron-proton effective mass splitting appear
particularly interesting. A more repulsive $EOS$ for neutron matter at high
baryon densities is expected. Effects on new critical properties of warm $ANM$,
mixing of mechanical and chemical instabilities and isospin distillation, are
also presented. The $\delta$ influence is mostly on the {\it isovectorlike}
collective response.
  The results are largely analytical and this makes the physical meaning quite
transparent. Implications for nuclear structure properties of drip-line nuclei
and for reaction dynamics with Radioactive Beams are finally pointed out.
