  In the framework of the quasipotential method the covariant expression for
the two-particle vertex operator is obtained. The nuclear structure corrections
of orders (Z\alpha)^4, (Z\alpha)^5 including recoil effects to gyromagnetic
factors of the bound electron and muon are calculated. Numerical value of the
contribution of order (Z\alpha)^5 is obtained by means of the dipole
parameterization for the nuclear charge form factor in the range of the nuclear
charges Z=7-32.
