Abstract In this work, we study magnetic excitations of amorphous ferromagnetic alloys (40Fe40Ni14P6B11 and 48Fe34Ni18P) by small-angle polarized neutron scattering in geometry when a magnetic field is inclined toward the neutron beam direction. The polarized neutrons are used in order to extract the scattering arising from the spin waves only. In this case, the energy-integrated neutron cross-section contains a part, which depends on neutron polarization and has a left-right asymmetry in the plane determined by the directions of the field and the neutron beam. The polarized SANS measurements on spin waves in amorphous FeNi alloys were performed at different values of an external magnetic field H and neutron wavelength λ. It is shown that the spin waves spectrum is quadratic in terms of the momentum transfer, and contains the gap of both the field and non-field nature: ε = Aq2 + gμBH + Δ0. We show that only by measuring simultaneously two dependencies of the cut-off angle θc – on the applied magnetic field and the neutron wavelength – it is possible to obtain reliable information about the spin-wave stiffness and the spin-wave gap in the amorphous ferromagnetic system.