Dynamic (time) characteristics of adaptive optics (AO) systems operating in a turbulent atmosphere are analyzed using analytical calculations of the Strehl ratio based on results of the theory of optical wave propagation in randomly inhomogeneous media. The analysis involves the model of the active mirror-corrector. The traditional AO system with a finite actuation time is described as a dynamic system with constant delay. In such a system, the permissible time delay is comparable with the time of transport of turbulent inhomogeneities by wind with the mean velocity to a distance equal to the coherence radius. An expression relating in a single formula the most important parameters of the system (the accuracy and operation frequency of the wavefront sensor and the aperture size of the optical system) and the atmosphere parameters (the Fried parameter and wind velocity with the achievable level of the Strehl ratio) is obtained. The differences between two types of tracking loops (open and closed) in AO systems are analyzed. Possibilities of the predictive algorithm for adaptive correction are demonstrated.