  In the framework of a Fermi liquid theory it is considered the possibility of
appearance of spin polarized states in strongly asymmetric nuclear matter with
Skyrme effective interaction. The zero temperature dependence of neutron and
proton spin polarization parameters as functions of density is found for SLy4,
SLy5 effective forces. It is shown that at some critical density it will be
formed the state with the oppositely directed spins of neutrons and protons,
while the state with the same direction of spins does not appear. In comparison
with neutron matter, even small admixture of protons strongly decreases the
threshold density of spin instability. It is clarified that protons become
totally polarized within very narrow density domain while in the density
profile of neutron spin polarization parameter their appear long tails near the
transition density.
