A rack serving unit comprises a carriage which may be moved along a rack aisle on substantially horizontal carrying rails. Carried along by the carriage there is a lifting platform which is suspended on the carriage by way of at least two traction mechanisms, preferably cables, and may be moved in the vertical direction with respect to the carriage. To stabilise the lifting platform against undesired lateral movements, a stabilising device is provided which comprises at least one guide element extending substantially horizontally parallel to the translatory movement path of the lifting platform. This guide element is in constant engagement with the lifting platform in such a way that the position of this latter in the direction of the translatory movement is constantly defined. Provided at both ends of the translatory movement path, there is a lifting device for each guide element by means of which the guide element may be moved synchronously with the lifting platform in the vertical direction.