A nonlinear time-series analysis method is used to investigate the dynamic behavior of the estrous cycle in female mice. Taking the daily changes in the cell types observed in the vaginal smears of mice as a single-variable time series, we construct a multi-dimensional state space by using an embedding scheme. The Lyapunov exponent and the correlation dimension of the trajectories in the re-constructed state space are analyzed in order to understand the underlying dynamics of the reproductive cycle of the mice. The time-series analysis results are found to be consistent with the physiological description of the reproductive endocrine system. Moreover, the results suggest that the variations in the estrous cycle of mice have a low-dimensional chaotic motion.