  Radiative-recoil corrections to hyperfine splitting in muonium of orders
$\alpha(Z\alpha)(m/M)^2E_F$ and $(Z^2\alpha)(Z\alpha)(m/M)^2E_F$ are
calculated. These corrections are of the second order in the small
electron-muon mass ratio. An analytic expression $[(-6 \ln2- \frac{3}{4})\alpha
(Z\alpha) - \frac{17}{12} (Z^2 \alpha) (Z\alpha)](\frac{m}{M})^2 E_F$ is
obtained. Numerically the correction is equal to $-0.0351\:\mbox{kHz}$ and is
of the same order of magnitude as the expected accuracy of the current Los
Alamos experiment to measure the hyperfine splitting.
