A new measurement method for second-order nonlinear after-effect function has been developed. Theoretical calculation starting from a general time-evolution equation connects nonlinear responses in time domain and frequency domain and thus gives the nonlinear response to applied external field of arbitrary form. In addition, it turns out in the frequency domain that the dc component of a second-order nonlinear response function corresponds to a linear response function. For example, the dc component of the electric birefringence relaxation is equivalent to the dielectric relaxation. This simple relation indicates an advantage of a frequency-domain measurement for nonlinear responses. As an example, the electric birefringence relaxation is measured in two-dimensional frequency domain for aqueous solution of sodium poly(styrenesulfonate) to confirm the validity of the theoretical results.