Analytic calculation of the hyperfine coupling tensors for multi-configurational quasi-degenerate perturbation theory is developed based on the Lagrange multiplier formalism. Calculation of Lagrange multipliers is not required if the corresponding constraining conditions do not depend explicitly on the magnetic moments of the nuclei. Except for the explicit form of the one-electron perturbation operator, the derivation presented in this work is also applicable to other molecular properties for which the basis functions do not depend on the differentiation variable, and for which the dependence of the Hamiltonian is through a one-electron operator only. (C) 2003 American Institute of Physics.