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Methods for the determination of the frequency dependent hyperpolarizabilities, p (-26J; 6J, 6J), p (-6J; 6J, 0), and P (O; 6J,-6J) at the self-consistent field (SCF) level of theory are discussed and compared. Two efficient alternatives are proposed; one involves determination of appropriate response vectors which arise in first-order perturbation theory at frequency 6J, and the other involves solving first-order perturbation theory equations at frequency 0 (static), 6J and 26J. Neither approach involves solution of the second-order perturbation theory equations. The method is illustrated with application to formaldehyde and methyl fluoride using large one-particle basis sets. The basis set requirement for convergence of this property at the SCF level of theory is investigated. Basis sets including up to d functions on first row atoms and p functions on hydrogen incorporating diffuse functions appear to be adequate. The effect …