Abstract: In order to identify phase failure in an asynchronous machine, monitoring of the phase currents is performed, a trigger signal being generated for each phase in the event of a limit value being undershot. In order to cover the entire frequency range in converter operation, a changeover is made between different monitoring states. In the first monitoring state, the trigger signal is generated if the instantaneous value of the phase current in each case falls below the limit value. A changeover is then always made to the second monitoring state, where the duration of the trigger signal is compared with the swept angle of rotation of the voltage vector in the same phase. If the state of the phase current lasts during this period of time, in a third monitoring state the duration of the trigger signal or the continuance of the phase current state is checked during a defined delay time interval. If the trigger signal outlasts the delay time interval, phase failure is signaled.