  The nuclear equation-of-state is a topic of highest current interest in
nuclear structure and reactions as well as in astrophysics. In particular, the
equation-of-state of asymmetric matter and the symmetry energy representing the
difference between the energy densities of neutron matter and of symmetric
nuclear matter are not sufficiently well constrained at present. The density
dependence of the symmetry energy is conventionally expressed in the form of
the slope parameter L describing the derivative with respect to density of the
symmetry energy at saturation. Results deduced from nuclear structure and
heavy-ion reaction data are distributed around a mean value L=60 MeV.
  Recent studies have more thoroughly investigated the density range that a
particular observable is predominantly sensitive to. Two thirds of the
saturation density is a value typical for the information contained in
nuclear-structure data. Higher values exceeding saturation have been shown to
be probed with meson production and collective flows at incident energies in
the range of up to about 1 GeV/nucleon.
  From the measurement of the elliptic-flow ratio of neutrons with respect to
light charged particles in recent experiments at the GSI laboratory, a new more
stringent constraint for the symmetry energy at suprasaturation density has
been deduced. It confirms, with a considerably smaller uncertainty, the
moderately soft to linear density dependence of the symmetry energy previously
deduced from the FOPI-LAND data. Future opportunities offered by FAIR will be
discussed.
