Based on genetic and biochemical advances on the molecular mechanism of circadian rhythms, a computational model for the mammalian circadian clock is used to examine the dynamical bases of circadian-clock-related physiological disorders in humans. Entrainment by the light-dark cycle with a phase advance or a phase delay is associated with the Familial advanced sleep phase syndrome (FASPS) or the Delayed sleep phase syndrome (DSPS), respectively. Lack of entrainment corresponding to the occurrence of quasiperiodic oscillations with or without phase jump can be associated with the non-24 h sleep-wake syndrome. In the close vicinity of the entrainment domain, the model uncovers the possibility of infradian oscillations of very long period. Perturbation in the form of chronic jet lag, as used in mice, prevents entrainment of the circadian clock and results in chaotic or quasiperiodic oscillations. It is important to clarify the conditions for entrainment and for its failure because dysfunctions of the circadian clock may lead to physiological disorders, which pertain not only to the sleep-wake cycle but also to mood and cancer.