The implementation of frequency-dependent second hyperpolarizabilities is presented using the time-dependent (spin-)restricted open-shell Hartree-Fock (TDROHF) theory (ROHF cubic response theory). The expression for the ROHF cubic response function (frequency-dependent second hyperpolarizability) is derived based on the quasienergy derivative (QED) method. We present an application of the ROHF cubic response theory to the frequency-dependent second hyperpolarizabilities of ground states of open-shell atoms (which are in S states) [Li(S-2), Na(S-2), K(S-2), and N(S-4(o))] for various third-order optical processes.