The possibility of appearance of spin polarized states in strongly asymmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with the Skyrme effective interaction. The zero temperature dependence of the neutron and proton spin polarization parameters as functions of density is found for SLy4 and SLy5 effective forces. It is shown that at some critical density strongly asymmetric nuclear matter undergoes a phase transition to 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 a very narrow density domain while the density profile of the neutron spin polarization parameter is characterized by the appearance of long tails near the transition density.