Calculations of the magnetizabilities and the rotational g factors at the self-consistent-field (SCF) and second-order Moller-Plesset perturbation theory (MP2) levels of theory are reported for H-2, N-2, F-2, HF, CO, HCN, HNC, H2O, and NH3. The sums rules, that verify the reliability of the calculations, are shown to be well satisfied. The second-order correlation corrections to the magnetizabilities are found to be small, thus substantiating the generally observed good agreement between the experimental and SCF results. Vibrational corrections to the properties of the diatomic molecules are given. Very good agreement is found between the experimental and vibrationally corrected MP2 rotational g factors for the diatomic molecules.