Method for managing an automatic shutdown of a thermal engine belonging to a traction chain of a motor vehicle further comprising an automatic gearbox and an automatic start and stop system of the heat engine , in which: - following detection of a braking phase, in particular by detection of pressing on a brake pedal modifying a pressure (PMC) in a braking circuit, said method comprises an initial phase d the wait in which a speed (V_veh) of the motor vehicle is compared with a distinct high speed threshold (S_h) and a low speed threshold (S_b), and - in the case where the speed (V_veh) of the motor vehicle is greater than or equal to the high speed threshold (S_h), said method enters a phase of monitoring an activity on the brake pedal and if this activity is stable over a threshold duration (D_s), said activity being considered stable if a pressure signal (PMC) in the braking circuit is between a lower gauge (G_i) and a higher gauge (G_s) during the threshold duration (D_s), automatic shutdown of the thermal engine is authorized, or - in the case where the speed (V _ veh) of the motor vehicle is less than or equal to the low speed threshold (S _ b) said method enters a phase of monitoring an overpressure on the brake pedal and if an overpressure on the pedal is detected, said overpressure being detected when the pressure (PMC) in the braking circuit becomes higher at a threshold ( S_arr ) said threshold (S _ arr) being equal to a value of the pressure (PMC) in the braking circuit At moment when the speed (V _ veh) of the motor vehicle becomes lower Or equal to the low speed threshold (S_b) increased of an offset value , a automatic shutdown of the thermal engine is authorized - in the case where we are in the phase of monitoring an activity on the brake pedal and the speed of the motor vehicle (V_veh) becomes less than or equal to the low speed threshold ( S_b) without any stable activity on the brake pedal having been detected, then the method comprises the step of passing into the phase of monitoring an overpressure on the brake pedal . - following detection of a braking phase, in particular by detection of pressing on a brake pedal modifying a pressure (PMC) in a braking circuit, said method comprises an initial phase d the wait in which a speed (V_veh) of the motor vehicle is compared with a distinct high speed threshold (S_h) and a low speed threshold (S_b), and - in the case where the speed (V_veh) of the motor vehicle is greater than or equal to the high speed threshold (S_h), said method enters a phase of monitoring an activity on the brake pedal and if this activity is stable over a threshold duration (D_s), said activity being considered stable if a pressure signal (PMC) in the braking circuit is between a lower gauge (G_i) and a higher gauge (G_s) during the threshold duration (D_s), automatic shutdown of the thermal engine is authorized, or - in the case where the speed (V _ veh) of the motor vehicle is less than or equal to the low speed threshold (S _ b) said method enters a phase of monitoring an overpressure on the brake pedal and if an overpressure on the pedal is detected, said overpressure being detected when the pressure (PMC) in the braking circuit becomes higher at a threshold ( S_arr ) said threshold (S _ arr) being equal to a value of the pressure (PMC) in the braking circuit At moment when the speed (V _ veh) of the motor vehicle becomes lower Or equal to the low speed threshold (S_b) increased of an offset value , a automatic shutdown of the thermal engine is authorized - in the case where we are in the phase of monitoring an activity on the brake pedal and the speed of the motor vehicle (V_veh) becomes less than or equal to the low speed threshold ( S_b) without any stable activity on the brake pedal having been detected, then the method comprises the step of passing into the phase of monitoring an overpressure on the brake pedal . <EOS>