The relaxation spectra of the linear and nonlinear dielectric constants of the antiferroelectric Liquid crystals have been studied in their SmA, SmC* and SmCA* phases. In the SmA phase near the boundary to the SmC* or SmCA* phase, both the dielectric constants show a critical behavior due to the softening of the ferroelectric soft mode. In the SmC* phase, we obtain the third-order nonlinear spectrum of a higher-order Debye type with a negative increment, which corresponds to the ferroelectric Goldstone mode observed also in the linear spectrum. In the SmCA* phase, the antiferroelectric Goldstone mode is observed not in the linear spectrum, but in the third-order spectrum as a Debye-type relaxation with a positive increment. All these spectra can be analyzed in terms of simple phenomenological models.