The Green's functions technique suitable for broken symmetry structure analysis was developed. With the help of this new technique the phonon subsystem was analysed in ultrathin films and in cylindrical nanotubes with finite height. The most interesting results of mentioned analyses are spatial dependence of thermodynamical characteristics, existence of phonon gap and extremely low specific heat and thermal conductivity at low temperatures. This promises wide application of films and finite nanotubes in technology. The same technique was applied to investigate electron subsystems in rectangular nanostructures of all dimensions as well as in simple and full nanotubes. The most interesting conclusion of these analyses is the presence of autoreduction effect being the consequence of nonisomorphic transition configuration - momentum space. This effect represents a qualitative difference between nano and macroscopic structures. The skin effect is present in all types of nanostructures except nano-parallelepiped where antiskin effect takes place. The latter is quite understandable, since in nano-parallelepiped nodes are on boundaries.