Sleep inertia refers to the period of reduced vigilance following upon awakening from sleep. To investigate the time course of sleep inertia, self-ratings of alertness and reaction time in a memory task were repeatedly assessed after nighttime and daytime sleep episodes in healthy young men. Alertness gradually increased and reaction time gradually decreased within the first hour after awakening. Their time course could be described by exponential functions with time constants of 0.45 h and 0.3 h, respectively. The data demonstrate that sleep inertia is a robust, quantifiable process that can be incorporated in models of sleep and vigilance.