Within the framework of the quantum theory of polarized line formation, in the limit of complete frequency redistribution and of the collisionless regime, we derive explicit formulae describing the statistical equilibrium and the radiative emission of a multiterm atom with hyperfine structure, in the presence of an external magnetic field. The formulae we obtained for the radiative rates of the statistical equilibrium equations and for the radiative coefficients of the transfer equation for polarized radiation can be applied to investigate the formation of spectral lines for which both fine-structure and hyperfine-structure effects are important (e.g., the D1 and D2 lines of Na I in the solar atmosphere).