A satellite-based SAR system having a space segment with a plurality of satellites and a ground segment with one or a plurality of ground stations is provided. A satellite receives a position report from an emergency transmitter in its service area and forwards it to a ground station. The ground segment stores the position of the emergency transmitter, received with the last position report, in a management system for emergency transmitters. The emergency transmitter sends position reports to the satellite such that the reception of position reports at the satellite is coordinated such that at any time only position reports arrive which differ with regard to their signal parameters such that simultaneous reception is possible. A rescue operation is initiated for the emergency transmitter if no deactivation message has been received from the emergency transmitter and no position report is received from the emergency transmitter within a specified period.