This work studies the magnetic excitations of amorphous ferromagnetic alloys (Fe40Ni40P1411B6 and Fe48Ni34P18) by small-angle polarized neutron scattering in the geometry when the magnetic field is inclined towards the neutron beam direction. 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 component 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. Small-angle polarized neutron scattering measurements on spin waves in amorphous iron–nickel alloys were performed at different values of the external magnetic field H and neutron wavelength λ. The spin-wave spectrum is quadratic in terms of the momentum transfer and contains both a field gap and an inherent gap Δ of a non-field nature: Eq = Aq2 + gμBH + Δ. Only by measuring simultaneously two dependencies of the cut-off angle θc – on the applied magnetic field and on the neutron wavelength – is it possible to obtain reliable information about the spin-wave stiffness and the spin-wave gap in these amorphous ferromagnetic systems.