This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.