The invention relates to an elevator system for the transport of loads and/or persons in an elevator shaft with at least two elevator cars which can be moved in the elevator shaft and are connected to a counterweight via carrying means, wherein a drive is associated with each car. In order to develop the elevator system further in such a manner that it can be produced inexpensively and has an improved transport capacity it is suggested in accordance with the invention that at least one common track section and, in addition, separate track sections arranged next to one another be associated with at least two cars in sections along the elevator shaft, wherein the cars can be moved not only in the same direction but also in directions opposite to one another.