Method for predictively influencing a vehicle speed, wherein the vehicle speed is influenced on a route with a changing parameter within a predefined speed corridor, wherein segments with a defined segment length and speed sections are used, wherein the route lying ahead is divided into segments (S), to which various speed sections (GA) are assigned, wherein segment values and speed values which intersect in a two-dimensional diagram are defined as nodes, and wherein each node is to be assigned a discrete position on the vehicle's route lying ahead in conjunction with a discrete speed, wherein at least one entry can be stored for each node in storage medium, wherein a cost value can be stored for the respective node, and wherein cost values which are stored for a plurality of nodes in the storage medium are compared with new cost values in order to determine a cost-optimum vehicle speed on a route, characterized - in that in a first step an entry is made in the storage medium, for a current node (Ka) which represents the current position and speed of the vehicle, - in that in a second step the speeds which can be reached within a segment length are calculated so that a plurality of possible subsequent nodes (Kn) which can be reached from the current node are determined, - in that in a third step travel-through costs (Kan) are calculated for each subsequent node (Kn), wherein the values stored in the storage medium are compared in order to determine the optimum vehicle speed, - in that in the third step, if there is no entry for the subsequent node (Kn) in the storage medium, an entry of the subsequent node (Kn) is produced which contains a cost value (Wkn), wherein if there is an entry for the subsequent node (Kn) in the storage medium, and the cost value (Wkn) which is already stored is higher than the cost value (Wkn') of the new node, the existing cost value (Wkn) is replaced by the new cost value (Wkn'), and - in that each node can be assigned a discrete position on the route lying ahead, in conjunction with a discrete speed within a speed corridor, and in that in the second step within the speed corridor, which can be reached within a segment length, are calculated. - in that in a first step an entry is made in the storage medium, for a current node (Ka) which represents the current position and speed of the vehicle, - in that in a second step the speeds which can be reached within a segment length are calculated so that a plurality of possible subsequent nodes (Kn) which can be reached from the current node are determined, - in that in a third step travel-through costs (Kan) are calculated for each subsequent node (Kn), wherein the values stored in the storage medium are compared in order to determine the optimum vehicle speed, - in that in the third step, if there is no entry for the subsequent node (Kn) in the storage medium, an entry of the subsequent node (Kn) is produced which contains a cost value (Wkn), wherein if there is an entry for the subsequent node (Kn) in the storage medium, and the cost value (Wkn) which is already stored is higher than the cost value (Wkn') of the new node, the existing cost value (Wkn) is replaced by the new cost value (Wkn'), and - in that each node can be assigned a discrete position on the route lying ahead, in conjunction with a discrete speed within a speed corridor, and in that in the second step within the speed corridor, which can be reached within a segment length, are calculated. <EOS>