  We consider hyperfine splitting of 1s and, in part, of 2s levels in light
hydrogen-like atoms: hydrogen, deuterium, tritium, helium-3 ion, muonium and
positronium. We discuss present status of precision theory and experiment for
the hfs intervals. We pay a special attention to a specific difference, D_{21}
= 8 E_{hfs}(2s) - E_{hfs}(1s), which is known experimentally for hydrogen,
deuterium and ^3He^+ ion. The difference is weakly affected by the effects of
the nuclear structure and thus may be calculated with a high accuracy. We
complete a calculation of the fourth order QED contributions to this difference
and present here new results on corrections due to the nuclear effects. Our
theoretical predictions appear to be in a fair agreement with available
experimental data. Comparison of the experimental data with our examination of
D_{21} allows to test the state-dependent sector of theory of the hfs
separation of the 1s and 2s levels in the light hydrogen-like atoms up to
10^-8.
