  The lattice dynamics of low-frequency rigid-plane modes in metallic (graphene
multilayers, GML) and in insulating (hexagonal boron-nitride multilayers, BNML)
layered crystals is investigated. The frequencies of shearing and compression
(stretching) modes depend on the layer number ${\EuScript N}$ and are presented
in the form of fan diagrams. The results for GML and BNML are very similar. In
both cases only the interactions (van der Waals and Coulomb) between
nearest-neighbor planes are effective, while the interactions between more
distant planes are screened. A comparison with recent Raman scattering results
on low-frequency shear modes in GML [Tan {\it et al.}, arXiv:1106.1146v1
(2011)] is made. Relations with the low-lying rigid-plane phonon dispersions in
the bulk materials are established. Master curves which connect the fan diagram
frequencies for any given ${\EuScript N}$ are derived. Static and dynamic
thermal correlation functions for rigid-layer shear and compression modes are
calculated. The results might be of use for the interpretation of friction
force experiments on multilayer crystals.
