Terms contributing to the hyperfine structure of the muonium ground st
ate at the level of few tenths of kHz have been evaluated. The alpha2(
Zalpha) radiative correction has been calculated numerically to the pr
ecision of 0.02 kHz. Leading ln(Zalpha) terms of order alpha4-n(Zalpha
)n,n = 1,2,3, and some relativistic corrections have been evaluated an
alytically. The theoretical uncertainty is now reduced to 0.17 kHz. At
present, however, it is not possible to test QED to this precision be
cause of the 1.34 kHz uncertainty due to the muon mass.