  A relativistic wave equation for bound states of two fermions with arbitrary
masses which are exposed to a magnetic field is derived from quantum
electrodynamics. The interaction kernels are based upon the generalized
invariant M-matrices for inter-fermion and fermion-field interactions. As an
application we calculate the energy corrections in a weak homogeneous B field
to obtain the Zeeman splitting of the hyperfine structure and g-factors in the
lowest order (i.e. to alpha^4). Lande g-factors are presented for several of
the first excited states of hydrogen, muonium, and muonic-hydrogen.
