Superionic conductors exhibit non-Debye behavior of solid dielectrics at low frequencies (f9Hz). Based on the characteristic of superionic conductors and a physical picture of Ngai's infrared divergent theory, we consider the fast ion transport as a non-Markovian process and analyze the alternating current properties of superionic conductors. The theory predicts that the admittance diagram is a line the curvature of which is less than one at higher frequencies. The discrepancy between theory and experiments at lower frequencies is due to interfacial effects.