  A relativistic theory of the Zeeman splitting of hyperfine levels in
two-fermion systems is presented. The approach is based on the variational
equation for bound states derived from quantum electrodynamics [1].
Relativistic corrections to the g-factor are obtained up to O(alpha^2).
Calculations are provided for all quantum states and for arbitrary fermionic
mass ratio. In the one-body limit our calculations reproduce the formula for
the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results
will be useful for comparison with high-precision measurements.
