An elevator system has a car assembly including a first elevator car, a second elevator car, a counterweight, and a drive machine unit having a traction sheave and a traction device guided over the traction sheave. The traction device is connected to the car assembly and the counterweight on opposite side of the traction sheave. An adjustment mechanism enables the second elevator car to be adjusted in relation to the first elevator car within the car assembly. The adjustment mechanism has an adjustment device, a first adjustment traction device and a second adjustment traction device. The first adjustment traction device and the second adjustment traction device are guided over the adjustment device. The first adjustment traction device and the second adjustment traction device are connected to the second elevator car on one side of the adjustment device and to the counterweight on the other side.