Various approximate methods for the calculation of vibrational second hyperpolarizabilities are assessed on the basis of results or CH4, NH3, H2O, HF, and CO2. Three specific variations of the perturbation-theoretic approach are analyzed. These are defined by the types of terms retained in expansions which involve electrical and mechanical anharmonicities. The lowest-order approximation being the double-harmonic one and the next higher one the relaxation method. For the dynamic hyperpolarizabilities, the replacement of the optical frequencies (omega) by omega-->(infinity) (the infinite-frequency approximation) is also explored. On the evidence at hand it is concluded that the relaxation/infinite-frequency method is a satisfactory approximation for the nonlinear optical vibrational hyperpolarizabilities.