  We theoretically study the effect of exchange interaction on the
non-equilibrium spin waves in disordered paramagnetic metals under the spin
injection condition. We show that the gapless spectrum of spin waves,
describing the spin precession in the absence of the applied magnetic field,
changes sign to negative on the paramagnetic side near the ferromagnet -
paramagnet phase transition. The damping of spin waves is small in the limit
when electron-electron exchange energy is larger than the inverse electron mean
free time, while in the opposite limit the propagation of spin waves is
strongly suppressed. We discuss the amplification of the electromagnetic field
by the non-equilibrium spin waves.
