The relation between the rotational g-factor and the electric dipole moment of a diatomic molecule is investigated. An explicit expression for the irreducible nonadiabatic contribution in terms of excited electronic states is derived. The importance of this expression for the analysis of vibration-rotational spectra of diatomic molecules is discussed and explicit expressions are presented for the first two fitting parameters in an expansion of the nonadiabatic rotational term in an effective vibration-rotational Hamiltonian. Results of ab initio self-consistent field, multiconfigurational self-consistent field and second-order polarization propagator approximation calculations of nonadiabatic contributions to rotational g-factors of hydrides and fluorides of Li, B, Al, Ga and monoxides of C, Si and Ge are presented. Problems connected with usage of finite basis sets of one-electron functions in these calculations are discussed.