An elevator installation for zonal operation in a building, a method for zonal operation of such an elevator installation and a method for modernization of an existing elevator installation, in which the building is divided into several zones. The elevator installation includes several elevators for the transport of persons/goods in cages. A zone is associated with each elevator. At least one changeover storey for the changing over of persons/goods between cages of different zones is arranged between the zones. At least one elevator comprises at least two cages which are arranged one above the other and which are movable independently of one another at a pair of guide rails.