TN-LCDs doped with metal nanoparticles such as Pd, Ag, and Au are shown to exhibit a frequency modulation response together with the ordinary root-mean-square response to operating voltages. These devices are called FM-LCDs. The frequency range in this phenomenon spreads from several tens Hz to several thousands Hz depending on the materials of nanoparticles, their diameters, and their concentrations. The central frequency of each FM-LCD almost coincides with the dielectric relaxation frequency. FM-LCDs shows a sensitivity to the high frequency component of the driving voltage, this in turn gives rise to a fast electrooptic response in ms and sub-ms order. The EO effect of the FM-TN-LCD effect is explained based on the Maxwell and Wagner effect and it is shown that the metal nanopatricles have the effective electrical conductivity of sigma(2) = 6.0 x 10(5) S/m that is about 100 times smaller that of metal Ag.