The theory for the calculation of the frequency‐dependent hyperpolarizabilities β(−2ω; 0, ω), β(−ω; 0, ω), and β(0; ω, −ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time‐dependent Hellmann–Feynman theorem (e.g., the self‐consistent field [SCF] or the exact wave function). Using second‐order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency‐dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency‐dependent contribution may be more significant, such as for secondharmonic generation. Copyright © 1992 John Wiley & Sons, Inc.