Spin waves in a non-ferromagnetic electron liquid in a magnetic field are studied in the random phase approximation. The electron bound states in the field of impurity atoms are considered. It is shown that electron localization facilitates the propagation of spin waves. New branches of wave spectrum are found in the frequency region where propagation of Silin’s waves is not possible. The spectrum and damping decrement of waves are obtained. Intersection of the dispersion curve for a Silin wave with the resonance frequency of electron transitions between Landau levels and local levels results in a cross situation typical of coupled waves. The differential cross-section of magnetic scattering of neutrons by a two-dimensional electron liquid in a magnetic field is calculated. The energy spectrum of scattered neutrons contains additional peaks associated with one-particle excitations of localized electrons and spin waves. The positions and widths of these peaks provide information about the spectrum of electron impurity states as well as the spectrum and damping of spin waves. ©1998 American Institute of Physics.