A method performed on-board by a satellite for processing a signal received from a terminal during a current time interval, includes receiving, during the current time interval, a main signal containing a message from a terminal, each message having a priority level; sampling the main signal to obtain samples; storing the obtained samples into the satellite memory; first demodulating the messages corresponding to the current time interval contained in the samples stored in memory; when the satellite is in the range of a ground station, transmitting to the ground station the content of the memory. The first demodulating includes, for each message of the messages contained in the samples and by priority order: demodulating and decoding the message; forwarding, using direct link or inter-satellite-link, the demodulated message to a ground station; estimating the number of remaining non-demodulated messages in the samples stored in the memory.