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In the framework of the quasipotential method in quantum electrodynamics wecalculate the contribution of light pseudoscalar (PS) and axial-vector (AV)mesons to the interaction operator of a muon and a proton in muonic hydrogenatom. The coupling of mesons with the muon is via two-photon intermediatestate. The parametrization of the transition form factor of two photons into PSand AV mesons, based on the experimental data on the transition form factorsand QCD asymptotics, is used. Numerical estimates of the contributions to thehyperfine structure of the spectrum of the S and P levels are presented. It isshown that such contribution to the hyperfine splitting in muonic hydrogen israther important for a comparison with precise experimental data.

The contribution of pseudoscalar and axial-vector mesons to hyperfine structure of muonic hydrogen