  We propose the semiclassical quantization for complicated electron systems
governed by a many-band Hamiltonian. An explicit analytical expression of the
corresponding Berry phase is derived. This impact allows us to evaluate the
Landau magnetic levels when the rigorous quantization fails, for instance, for
bilayer graphene and graphite with the trigonal warping. We find that the
magnetic breakdown can be observed for the certain type of classical electron
orbits.
