The characteristic modification of the spectrum of the exchange spin waves has been revealed in ferromagnet/ferromagnet multilayer films with a thickness of N(d1 + d2) by the spin-wave resonance method. This modification is due to the first bandgap at the wavenumber kb = π/(d1 + d2) of a magnon crystal, which is formed by one-dimensional modulation of the magnetization. It has been shown that the transformation of the multilayer film with thermal annealing to the film of a single-phase alloy is accompanied by the disappearance of this modification of the spectrum.