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In the framework of the quasipotential method in quantum electrodynamics wecalculate corrections to the nuclear structure proportional to $r_N^2$ fromtwo-photon exchange amplitudes in the fine and hyperfine structure of P-statesin muonic hydrogen, as well as the photon-photon interaction amplitudes,leading to the exchange of the axial vector meson. In constructing thequasipotential of the muon-nucleus interaction, we use the method of projectionoperators on states of two particles with a definite spin and total angularmomentum. Analytical calculation of the matrix elements is performed andcontributions to the fine and hyperfine structure of the $2P_{1/2}$ and$2P_{3/2}$ levels are obtained.

Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen