In this work, the effects from one-pion exchange in ep and mu p bound states by two-photon coupling are discussed. We at first calculate the effective couplings of a pion with a lepton (electron or muon) by two-photon coupling and the corresponding effective nonrelativistic potential. Then we calculate its corrections to the hyperfine structure of 2S and 2P states. We find that the corrections to the hyperfine structures of electronic hydrogen's 2S and 2P states and muonic hydrogen's 2P state are small and can be neglected, while the correction to the hyperfine structure of muonic hydrogen's 2S state Delta E-HFS(2S) (F = 1, mu p) is about 0.0028 meV. And after some further discussion we suggest that the similar exchange of a scalar meson such as sigma between mu p by two-photon coupling may give a much larger contribution to the Lamb shift of muonic hydrogen.