Absorption spectra in ferrospinel single crystal films prepared by the method of chemical transport reactions are considered. It is demonstrated that additional absorption peaks in the absorption spectra are registered with an EPR spectrometer in manganese and magnesium-manganese ferrite films magnetized parallel to their surfaces. Interpreting these peaks as magnetostatic fluctuations, the wave numbers, group velocities, and attenuation parameters are retrieved from experimental values of the saturation magnetization, crystallographic anisotropy constants, and magnetic fields of the observed modes. The common effects observed for the ferrospinel films are oscillations of the attenuation of magnetostatic fluctuations with frequency variations. A dependence of the pattern of attenuation oscillations on the strength of exchange interaction, spin pinning parameter, and surface anisotropy is established. Growth of the attenuation parameter and depth of exchange absorption oscillations with frequency is related with the efficiency of excitation of the exchange spin modes.