Regenerative fixed-bed processes are widely applied in chemical and environmental engineering. However, their theoretical analysis lags behind industrial implementation due to extremely time-consuming numerical simulation. Shortcut models have been introduced in order to facilitate efficient parametric analysis. Interestingly, independent approaches for different systems led to membrane processes as a generalized steady-state analogon of regenerative processes. Despite the successful application of the membrane analogy, a theoretical framework summarizing the common features of the different cases has been missing so far and existing reduced models rely on arbitrary assumptions. The present paper introduces a general method to derive shortcut models of fast cycling processes preserving a maximum of the features of the original system. The feasibility of this approach is demonstrated using a reverse-flow reactor and a pressure-swing adosrption process as test cases.