A drive unit for an elevator installation having a first traveling body and a second traveling body, which traveling bodies are supported by a support device, drives the support device and thus the two traveling bodies. The two traveling bodies each have at least one first support roller by which the support device supports the traveling bodies, at least partially. The drive unit includes at least one first and one second roller arranged on a common axis of rotation of the drive unit, wherein at least one of the first or second rollers is a drive unit roller for driving the support device. On the way from the first traveling body to the second traveling body, the support device is guided over the first drive unit roller and over the second drive unit roller. The guidance is hereby such that the circumferential speeds of the two drive unit rollers vary.