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M. M. Nekhoroshev put forward the problem of to find the Complex Germ on aisotropic invariant torus with respect to Hamiltonian phases flows which comefrom k-functions in involution. This statement was partially solved in [9]establishing that if certain simplectic operator has a simple spectrum then thecomplex germ exist. In this work we solve this problem, providing a fullsolution, i.e. we present conditions for the existence and uniqueness ofcomplex germ through the monodromy operator constructed in [9], but without thesimple spectrum condition. We study also the Hamiltonian system with cyclicvariables.

Complex Germen on invariant isotropic tori under the Hamiltonian phases flow with in involution Hamilton functions