The multiconfiguration valence-bond method (VB) is applied to diatomic molecules using the Hartree-Fock (HF) atomic basis set. The hyperfine constant, Fermi contact term, is computed as a function of the interatomic separation for the X²Πground state of ¹⁷OH and X¹Σ ground state of ¹⁰⁷AgH⁺ molecules. This study leads to a number of conclusions about the influence of correlation and polarization effects on the hyperfine structure of hydrogenic molecules. The calculated values of the Fermi contact term are found to agree within 1 % of the experimental values wherever available.