A method for the exchange of data between one unit of an elevator system and a monitoring unit of a service center locationally remote from the elevator system, wherein, via a first communication network, the one unit is connected with a communication unit arranged on, or in, an elevator car that travels vertically in an elevator hoistway, and wherein the data that are transmitted by the one unit are transmitted to the communication unit and stored there. A mobile-communication end-device brought into the elevator car by an elevator passenger is connected, via a second wireless communication network, with the communication unit and the stored data are transmitted by the communication unit to the end-device, and stored in the latter. When the elevator car is exited by the elevator passenger with the end-device, the stored data are transmitted from the end-device via a public mobile-communication network to the monitoring unit.