Method for moving a line of vehicles having a first, leading motor vehicle and at least one second motor vehicle (4, 6, 8, 10, 12) electronically coupled to the first, leading motor vehicle, in which method the motor vehicles (4, 6, 8, 10, 12) are at least temporarily moved along a route at a predefinable constant longitudinal mutual distance (a) based on a predefinable overall operating strategy (line controller) assigned to the line of vehicles, characterised in that the overall operating strategy contains at least the following steps: a) If the first, leading motor vehicle s braked in a braking process triggered by the driver of the first, leading motor vehicle and/or automatically in the first, leading motor vehicle, the first, leading motor vehicle is initially braked with a first value for the longitudinal deceleration corresponding to a predefinable minimum longitudinal deceleration that is independent of a deceleration specification of the driver or of an automatically generated deceleration specification, then b) during the running braking process at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles is detected, and then c) the longitudinal deceleration of the first, leading motor vehicle is, during the running braking process, increased to a second value that is higher than the first value, and the at least one then appearing variable representing the longitudinal distance (d) between the at least two motor vehicles (2 to 12) of the line of vehicles is once again determined, and d) if it is then found that the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles has changed beyond a specific measure towards a decreasing longitudinal distance (d), the longitudinal distance of the first, leading motor vehicle is adjusted to a value in a range extending from the first value to the second value, and e) if it is then found, however that the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles has changed beyond a specific measure towards an increasing longitudinal distance (d) or has remained unchanged, the longitudinal deceleration of the first, leading motor vehicle continues to be increased during the running braking process until the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles does not change beyond a specific measure towards a decreasing longitudinal distance (d). a) If the first, leading motor vehicle s braked in a braking process triggered by the driver of the first, leading motor vehicle and/or automatically in the first, leading motor vehicle, the first, leading motor vehicle is initially braked with a first value for the longitudinal deceleration corresponding to a predefinable minimum longitudinal deceleration that is independent of a deceleration specification of the driver or of an automatically generated deceleration specification, then b) during the running braking process at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles is detected, and then c) the longitudinal deceleration of the first, leading motor vehicle is, during the running braking process, increased to a second value that is higher than the first value, and the at least one then appearing variable representing the longitudinal distance (d) between the at least two motor vehicles (2 to 12) of the line of vehicles is once again determined, and d) if it is then found that the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles has changed beyond a specific measure towards a decreasing longitudinal distance (d), the longitudinal distance of the first, leading motor vehicle is adjusted to a value in a range extending from the first value to the second value, and e) if it is then found, however that the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles has changed beyond a specific measure towards an increasing longitudinal distance (d) or has remained unchanged, the longitudinal deceleration of the first, leading motor vehicle continues to be increased during the running braking process until the at least one variable representing the longitudinal distance (d) between at least two motor vehicles (2 to 12) of the line of vehicles does not change beyond a specific measure towards a decreasing longitudinal distance (d).