An elevator installation includes an elevator cage carrier movable in a travel space provided for travel of the elevator cage carrier. Moreover, a first elevator cage and a second elevator cage are adjustably arranged at the elevator cage carrier and a drive unit arranged at the elevator cage carrier. In addition, an adjusting device with a first traction means and a second traction means guided in opposite directions around a drive roller, drivable by the drive unit, is provided. In that case the spacing between the first elevator cage and the second elevator cage is adjustable by movement of the elevator cages in opposite directions. An adaptation to different story spacings is thereby possible.