The invention concerns a method for transmitting digital messages through output terminals (22) of a monitoring circuit (18) incorporated in a microprocessor (12) during execution of a series of instructions, the digital messages representing characteristic data stored by the monitoring circuit upon detecting a specific event in the execution of the series of instructions, one of said data corresponding to an identifier of said specific event, said method comprising the following steps: comparing the data of the last two detected specific events having a common identifier, if the compared data are identical, incrementing a repeat counter associated with said specific event; and if the compared data are different, transmitting a digital message representing the data of the last detected specific event, and furthermore, if the content of the repeat counter associated with said specific event is other than zero, transmitting a digital message indicating a repeat of the specific event.