A current operational state of a program-controlled domestic appliance is monitored while it carries out an operating process. The monitoring system includes a retrofit module and a communication device separate from the retrofit module and from the domestic appliance. The retrofit module has a fastening arrangement for releasable fastening on an outer face of an appliance housing, a data exchange unit for wireless communication, and a sensor arrangement with a magnetic field sensor that detects a magnetic field that is generated by a drive motor of the domestic appliance and that penetrates outwards through the appliance housing. The system determines the current operational state of the domestic appliance with the aid of detected measured values of the magnetic field and outputs the state via the communication device.