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In this talk I present recent work on structure-preserving integration for multi- frequency oscillatory Hamiltonian systems by multi-frequency ARKN methods and multi-frequency ERKN integrators.The adjoint schemes for both ARKN methods and ERKN integrators are an- alyzed for achieving an effcient high-order symplectic and symmetric composition method.The high-order symplectic and symmetric composition methods are derived based on multi-frequency ARKN methods and ERKN integrators.