A simple one phonon model is used to treat the effects of the resonant polaron interaction on the de Haas-Van Alphen oscillations in polar semiconductors. It is shown that particular maxima of the magnetic moment occurring at E,/hw, = 1/2, 3/2, 5/2 etc, where E,, h o c are the Fermi and cyclotron energies respectively, are expected to be suppressed whenever the electron concentration is such that the resonant conditions w,/w, = 1, 2, 3 etc. where q, = lattice longwave optic mode frequency, are simultaneously satisfied.