An elevator system has two elevator cars arranged one over the other, but that can travel independently of each other. Both elevator cars are suspended on suspension and traction mechanisms and each is coupled to a separate counterweight. Both elevator cars have a lower cable, wherein the two lower cables are tensioned by separate tension devices. The lower cable of the first, lower elevator car is fastened to the first elevator car and the first counterweight, The lower cable of the second, upper elevator car is guided at the second elevator car and at least one of the two lower cable ends thereof is secured by a weighted body secured in place with play and/or free-floating.