Superionic conductor superlattices, which provide the mini-bands of relaxation modes (relaxons), give rise to a non-Debye type of dynamic conductivity. The frequency exponent s in Re sigma(omega) = sigma(0) + sigma(1) omega(s) is approximately given by a non-integer exponent alpha of the R-distribution, expressing the localization of particle, such that s = 1.5 - alpha for 1.5 > alpha greater than or equal to 0. The time dependence of conductivity is also precisely investigated.