Calculations of the hypermagnetizabilities (eta) at the self-consistent-field (SCF) and second-order Moller-Plesset perturbation theory (MP2) levels of theory are reported for H-2, N-2, HF, and CO. Electron correlation is found to be unimportant for H-2, but very important for the other three molecules. The individual components of eta are more affected by correlation effects than the hypermagnetizability anisotropy (Delta eta) which mediates the birefringence of a material in the presence of a magnetic field (the Cotton-Mouton effect). The zero-point-vibrational averaging, pure vibrational corrections, and frequency dependence are important for the individual components, but are less important for Delta eta due to cancellation between the various contributions. Excellent agreement is found with the previous theoretical results for H-2, but only fair agreement with the experimental results for N-2 and CO.