Low-frequency (LF) noise under cyclo-stationary excitation has received considerable attention recently. Until now, only semiempirical models for cyclo-stationary random telegraph signal (RTS) and flicker noise have been reported in the literature. In this paper, we report, starting from basics, the analytical nonstationary extension of the standard LF noise models. This analytical model is valid for any kind of periodic excitation. After a rigorous analysis, by introducing some suitable approximations, we identify the main reason behind nonstationary behavior. Our analysis clearly shows that, for almost all practical purpose, an averaged time constant and an averaged trap density can model the cyclo-stationarity of RTS and flicker noise, respectively.