Abstract: A method and device for effecting a fast but smooth deceleration or stopping of trains controlled under the automatic train control (ATC) system. Under ATC, a permitted maximum velocity is provided as an "ATC condition" to activate the brake system of the train if that velocity is exceeded. When it is necessary to alter the velocity of a train, a control center specifies a feeder section to have the ATC condition to be altered. Next, a substation corresponding to the specified feeder section is provided with notice about the alteration of the ATC condition. The notice includes the impending reduction of velocity. In response, the substation decelerates the train without using the ATC brake system provided on the train. When the train has been sufficiently slowed down such that the alteration of the ATC condition will not result in activation of the ATC brake system, the alteration of the ATC condition is then effected.