In a collisional plasma, fast and slow shocks are time stationary. They evolve in such a way that the flow variations remain small under the action of a small perturbation. By contrast, in the case of a trans-Alfv¿nic shock wave (TASW), at which the flow velocity passes over the Alfv¿ velocity, the small perturbation generates finite variation of the initial flow. As a result, the shock disintegrates or transforms into some other unsteady state. In the present paper, the problem of shock propagation is considered for a collisionless plasma with anisotropic pressure. Using a kinetic theory, it is shown that the transition of the flow velocity over the Alfv¿n velocity at a shock is crucial for its evolution. Namely, the small perturbation makes collisionless TASWs unsteady at timescales large enough compared to the ion gyroperiod. This conclusion is valid for both ordinary TASWs at which the Alfv¿n Mach number decreases and anomalous TASWs at which it increases. Possible manifestations of unsteady propagation of planetary bow shocks are discussed. ¿ 1999 American Geophysical Union