Received August 31, 2021, published online December 24, 2021
The nature of flexural rigidity of graphene monolayers and the formation of the quasi-flexural modes in graphite and graphene nanofilms is explained. It is shown, that in the major part of the band of quasi-continuous spectrum, quasi-flexural modes do not practically couple with the modes polarized in the plane of the layer. The frequencies of the propagone zone are determined for the phonons with various polarizations. The existence of a high-frequency propagation zone is demonstrated for quasi-flexural phonons. The conditions for the formation of quasi-local vibrations and boson peaks are analyzed for modes with different polarization. The conditions for the formation of the quasi-local vibrations and boson peaks in the modes of different polarization are analyzed.