The results of studying the possibility of measuring the energy gap of a nonfield nature in the spectrum of spin waves in ferromagnets are presented. As a research method, the technique of the small-angle scattering of polarized neutrons in inclined geometry is used, which allows one to separate the contribution of inelastic scattering. Inelastic scattering can be obtained as the difference between the intensities when the neutron beam is polarized along and against the direction of the magnetic field. Spin-wave scattering is concentrated in a cone limited by the cutoff angle θC. It is shown that the square of the cutoff angle linearly depends on the magnetic field H and the energy gap Δ of nonfield nature: . The parameter is inversely proportional to the constant spin-wave stiffness D of the material. Model calculations for the experiment on small-angle neutron scattering are presented. They convincingly show the possibility of measuring not only the spin-wave stiffness with an accuracy of several percent, but also the nonfield gap Δ with an accuracy of up to 1 μeV. The calculation technique is applied to the results of studying the classical Fe65Ni35 invar alloy at room temperature.