  Topology of levels of the quasiperiodic functions with m=n+2 periods on the
plane is studied. For the case of functions with m=4 periods full description
is obtained for the open everywhere dense family of functions. This problem is
equivalent to the study of Hamiltonian systems on the (n+2)-torus with constant
rank 2 Poisson bracket. In the cases under investigation we proved that this
system is topologically completely integrable in some natural sence where
interesting integer-valued locally stable topological characteristics appear.
The case of 3 periods has been extensively studied last years by the present
author, Zorich, Dynnikov and Maltsev for the needs of solid state physics
(''Galvanomagnetic Phenomena in Normal Metals''); The case of 4 periods might
be useful for Quasicrystals.
