  In the framework of a Fermi liquid theory it is considered the possibility of
ferromagnetic and antiferromagnetic phase transitions in symmetric nuclear
matter with Skyrme effective interaction. The zero temperature dependence of
ferromagnetic and antiferromagnetic spin polarization parameters as functions
of density is found for SkM$^*$, SGII effective forces. It is shown that in the
density domain, where both type of solutions of self--consistent equations
exist, ferromagnetic spin state is more preferable than antiferromagnetic one.
