  The corrections of order (Z alpha)^6m_1/m_2 and (Z alpha)^7 from one-loop
two-photon exchange diagrams to the energy spectra of the hydrogenic atoms are
calculated with the help of the Taylor expansion of corresponding integrands.
The method of averaging the quasipotential over the wave functions in the
d-dimensional coordinate space is formulated. The numerical values of the
obtained contributions to the fine structure of muonium, hydrogen and
positronium are presented.
