A description is given of the periodic-flow rotary regenerator, and it is contrasted to the other types of heat-exchanger systems which may be employed to “regenerate” or “recuperate” the exhaust-gas thermal energy in a gas-turbine plant. The advantages in principle of the periodic-flow type are considered briefly, and the mathematical complexities of analysis of the more exact theory of its performance are indicated. Available special solutions, obtained by numerical-graphical methods, provided by Hausen, Nusselt, Boestad, Iliffe, and Saunders and Smoleniec are reviewed and their limitations pointed out. An algebraic equation solution corresponding to the special case of high rotative speeds is shown to be exactly the same as the well-known equation for a direct-transfer-type counterflow exchanger. These results are supplemented with an “approximate theory” solution which has the advantage of being in closed form, and the limitations on accuracy of this solution are considered. Recommended design curves are presented using a set of simple nondimensional parameters, of the same nature as those employed for direct-transfer-type exchangers, and which are readily usable for the gas-turbine regenerator-design problem. The curves result from a rational extrapolation of the special case solutions of Hausen, employing the approximate theory as well as the results of Iliffe, to other situations of interest to the gas-turbine designer. An illustrative problem is included.