Spinodal instability in nuclear matter and finite nuclei is investigated. This instability occurs in the low-density region of the phase diagram. The thermodynamical and dynamical analysis is based on Landau theory of Fermi liquids. It is shown that asymmetric nuclear matter can be characterized by a unique spinodal region, defined by the instability against isoscalar-like fluctuation, as in symmetric nuclear matter. Everywhere in this density region the system is stable against isovector-like fluctuations related to the species separation tendency. Nevertheless, this instability in asymmetric nuclear matter induces isospin distillation leading to a more symmetric liquid phase and a more neutron-rich gas phase.