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We have studied an influence of Tamm plasmon-polaritons (TPPs) excitation on the nonlinear-optical response of one-dimensional photonic crystal/metal structures. It was shown that in case when the fundamental radiation is in resonance with the TPP, second-harmonic generation in the sample is enhanced over two times of magnitude in comparison with a bare metal film. Using methods of nonlinear transfer matrices it was demonstrated that the third-order nonlinear response of a metal/dielectric heterostructure, when both fundamental and third-harmonic radiation are in resonance with the first- and third-order TPPs respectively, can be enhanced via two mechanisms: fundamental field localization and optical harmonic resonant tunneling. The overall enhancement of the third harmonic generation in that case can exceed three orders of magnitude in comparison with the non-resonant case.