  We consider three-loop radiative-recoil corrections to hyperfine splitting in
muonium generated by diagrams with one-loop radiative photon insertions both in
the electron and muon lines. An analytic result for these nonlogarithmic
corrections of order $\alpha(Z^2\alpha)(Z\alpha)(m/M)\widetilde E_F$ is
obtained. This result constitutes a next step in the implementation of the
program of reduction of the theoretical uncertainty of hyperfine splitting
below 10 Hz.
