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The possibility of ferromagnetic and antiferromagnetic phase transitions insymmetric nuclear matter is analyzed within the framework of a Fermi liquidtheory with the effective Gogny interaction. It is shown that at some criticaldensity nuclear matter with D1S effective force undergoes a phase transition tothe antiferromagnetic spin state (the opposite direction of neutron and protonspins). The self--consistent equations of spin polarized nuclear matter withD1S force have no solutions, corresponding to the ferromagnetic spin ordering(the same direction of neutron and proton spins) and, hence, the ferromagnetictransition does not appear. The dependence of antiferromagnetic spinpolarization parameter as a function of density is found at zero temperature.Comment: Report at the workshop "Hot points in astrophysics and cosmology",  Dubna, August, 2-13, 2004. REVTeX4, 9 pages, 3 figure

Antiferromagnetic spin phase transition in nuclear matter with effective Gogny interaction