Control process of an alert and rescue system designed to be incorporated in the life jacket or suit of the crew member of a vessel, wherein the alert and rescue system comprises: actuation means connected to a control unit that activates a GPS (Global Positioning System) location device allowing to obtain the exact location of a shipwrecked person, a radio beacon adapted to emit a distress signal by radiofrequency, and the alert, a DSC selective calling device, and an AIS automatic identification device, wherein the control process is characterized in that it comprises the following stages: a) immediate activation of the alert system through actuation means connected to the control unit, after a MOB situation of man overboard occurring, b) constant emission of an alarm signal in the 121.5/243MHz frequency, by the radio beacon, alerting of the MOB situation to aircraft and vessels located within the range of said signal, c) execution of a first emergency call to the vessel where the shipwrecked person comes from, by the DSC selective calling device, alerting of the MOB situation, d) emission of the position of the shipwrecked person to any vessels situated within the VHF zone and recording of MMSI data of vessels situated within the VHF zone, by the AIS automatic identification device, e) execution of a second emergency call to the vessel where the shipwrecked person comes from using the DSC device, after the exact position of the shipwrecked person has been acquired through satellites by the GPS location device, f) selection by order of proximity the MMSI of the closest vessels previously identified by the AIS device, to later, through the DSC device, successively call each one of said vessel, vessel-to-vessel and through a communication channel if the vessel where shipwrecked person comes from does not respond to the DSC calls made by the shipwrecked person within a specific time period, and g) reception of an ACK confirmation signal, said confirmation signal being sent by the vessel where the shipwrecked person comes from, or by a vessel close to the shipwrecked person detected by the AIS automatic identification device, which have received some of the calls made by the DSC device; final rescue of the shipwrecked person; and manual switching off of the radio beacon, the DSC device and the AIS automatic identification device. actuation means connected to a control unit that activates a GPS (Global Positioning System) location device allowing to obtain the exact location of a shipwrecked person, a radio beacon adapted to emit a distress signal by radiofrequency, and the alert, a DSC selective calling device, and an AIS automatic identification device, a) immediate activation of the alert system through actuation means connected to the control unit, after a MOB situation of man overboard occurring, b) constant emission of an alarm signal in the 121.5/243MHz frequency, by the radio beacon, alerting of the MOB situation to aircraft and vessels located within the range of said signal, c) execution of a first emergency call to the vessel where the shipwrecked person comes from, by the DSC selective calling device, alerting of the MOB situation, d) emission of the position of the shipwrecked person to any vessels situated within the VHF zone and recording of MMSI data of vessels situated within the VHF zone, by the AIS automatic identification device, e) execution of a second emergency call to the vessel where the shipwrecked person comes from using the DSC device, after the exact position of the shipwrecked person has been acquired through satellites by the GPS location device, f) selection by order of proximity the MMSI of the closest vessels previously identified by the AIS device, to later, through the DSC device, successively call each one of said vessel, vessel-to-vessel and through a communication channel if the vessel where shipwrecked person comes from does not respond to the DSC calls made by the shipwrecked person within a specific time period, and g) reception of an ACK confirmation signal, said confirmation signal being sent by the vessel where the shipwrecked person comes from, or by a vessel close to the shipwrecked person detected by the AIS automatic identification device, which have received some of the calls made by the DSC device; final rescue of the shipwrecked person; and manual switching off of the radio beacon, the DSC device and the AIS automatic identification device.