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The spectrum of collective excitations of degenerate partially polarizedspin-1/2 fermions is considered. The spin-up fermions and the spin-downfermions are considered as different fluids. Corresponding two-fluidhydrodynamics consistent with a non-linear Pauli equation is suggested. Anequation of state for the spin current caused by the distribution of particleson different energy levels is suggested for the degenerate regime, where thespin current is caused by the Pauli blocking. Spectrum of three waves is foundas a solution of the hydrodynamic equations: two sound waves and one spin wave.Their spectrums are calculated for two regimes: propagation parallel andperpendicular to the direction of the equilibrium spin polarization.

Spin current contribution in the spectrum of collective excitations of  degenerate partially polarized spin-1/2 fermions at separate dynamics of  spin-up and spin-down fermions