In order to elucidate the hysteresis-free response (V-shaped response) observed at a transmittance of light in antiferroelectric smectic materials. the dynamical responses of the order parameters to an electric field are studied on the basis of an extended ANNNI model with J(3) < 0. It is shown that the V-shaped responses appear at mesophases with long period near the ferroelectric phase in low frequency range.