It was reported recently by us that the energy conversion efficiency)eta(ATG) of thermoelectric (TE) generators working under the alternating temperature gradient (ATG) produced by switching at an optimum period of tau = 120 or 240 s is several times higher than eta(STG) of them operating under the steady temperature gradient (STG), where the generators are sandwiched between two Peltier modules. However, the reason for eta(ATG) > eta(STG) has not yet been explained explicitly. In order to clarify the relation between the Optimum T and eta(ATG) or eta(ATG)/eta(STG) in the wide range of tau, long p- and n-type Cu/Bi-Te/Cu composites with t(Bi)-(Te) = 4.0 mm and t(cu) = 5.0 mm were fabricated so that they have an optimum tau longer than the previous periods. The maxima eta(ATG) of the p- and n-type composites were 0.073% at tau = 960 s and 0.057% at tau-480 s, respectively, and their eta(ATG)/eta(STG) were approximately 1.4. Owing to this experimental result, eta(ATG)/eta(STG) is related closely to the thermal diffusion time tau(D) of a composite or a generator, so that eta(ATG) and eta(ATG)/eta(STG) were found to be in inverse proportion to tau(D). The reason for this low eta(ATG) results from the high external resistance and the long tau caused by a thick t(Bi-Te), in addition to too fat Bi-Te sample giving the high thermal conductance. The maximum eta(ATG) was also found to be expressed successfully by a theoretical expression. (C) 2008 Elsevier Ltd. All rights reserved.