Parallel-connected UPS units of an online UPS system, which are each connected on the input side via a choke coil to an AC mains, in disconnectable fashion, and on the output side to a common load bus and whose supplied powers are individually variable, are disconnected from the AC mains in the event of a failure of the AC mains, at least if they are affected by the failure, and are successively reconnected to the AC mains after the restoration of the AC mains. In this case, in order to match the powers supplied by the individual UPS units to one another, while some of the UPS units are connected on the input side to the AC mains and others of the UPS units are not connected on the input side to the AC mains, a phase angle Δφ between the AC mains and the load bus is determined, and the power supplied by each of the UPS units which have not yet been reconnected to the AC mains is adjusted as a function of this phase angle Δφ.