The equation of motion for cracks which are subjected to stress pulses is derived by the Lagrangian method. An asymptotic solution is used to determine terminal crack velocity. The time in which essentially constant velocity will be reached is determined. The equation is further used to formulate a dynamic stability criterion. In addition to a critical stress a critical time of stress duration is of importance. Critical time and critical stress can be combined to a critical action. From this principle, a number of conclusions are derived which are used to explain a number of experimental facts for which a theoretical explanation was lacking hitherto.