A method for operating an engine automatic stop-start system used in a motor vehicle fitted with an internal combustion engine. The system allows: automatic stoppings of the engine when a set of conditions outside and inside the vehicle are satisfied; automatic startings of the engine following an automatic stopping when at least one engine demand condition is met. The method includes an internal value which is a count of a number of operations of the system, wherein the internal value is subjected to a high threshold and to a low threshold, and the method can modify at least one of the conditions outside or inside the vehicle if the internal value reaches the low threshold or reaches the high threshold.