An engine stopping and starting system for automatically stopping and starting an engine which comprises: a fuel injection controller for controlling the quantity of fuel to be injected by each of fuel injectors directly into a plurality of cylinders (12A-12D) and fuel injection timing thereof; an ignition controller for controlling ignition timing of spark plugs of the individual cylinders (12A-12D); an intake air quantity regulator for regulating the quantity of intake air introduced into each of the cylinders (12A-12D); an alternator driven by the engine; and a rotating speed sensing device (30, 31) for detecting engine speed; said engine stopping and starting system comprising: an automatic engine stop controller for automatically stopping the engine by interrupting fuel injection from the fuel injectors as necessary for keeping the engine running when predefined automatic engine stop conditions are satisfied, and an automatic engine restart controller for automatically restarting the engine by causing the fuel injector of at least one of the cylinders (12A-12D) which is on expansion stroke at engine stop and causing the spark plug of that cylinder to ignite a mixture produced therein when predefined engine restart conditions are satisfied; characterized in that said automatic engine stop controller sets a scavenging mode period for expelling in-cylinder exhaust gas in an early part of automatic engine stop control operation, the scavenging mode period being a period during which the fuel injection from the fuel injectors is interrupted and the quantity of intake air regulated by said intake air quantity regulator is set at a level higher than a minimum quantity of intake air necessary for keeping the engine running by a specific amount and the amount of electric power generated by said alternator is decreased compared to the amount of electric power generated before fulfillment of the automatic engine stop conditions, said automatic engine stop controller causes said intake air quantity regulator to decrease the quantity of intake air and causes said alternator to increase the amount of electric power generated thereby at a point in time when the engine speed drops down to a predetermined reference engine speed after setting the scavenging mode period, and wherein, in executing the automatic engine stop control operation, said automatic engine stop controller detects the TDC engine speed at a point in time when a specific period of time has elapsed after the engine speed has dropped down to the predetermined reference engine speed and, based on the detected TDC engine speed, said automatic engine stop controller sets the amount of electric power to be generated by said alternator to adjust the rate of engine speed decrease such that the piston of at least one of the cylinders (12A-12D) which is on expansion stroke at engine stop stops within a specified range suited for engine restart, and whereby the range is defined by 100° to 120° after the compression stroke TDC in terms of crank angle. an automatic engine stop controller for automatically stopping the engine by interrupting fuel injection from the fuel injectors as necessary for keeping the engine running when predefined automatic engine stop conditions are satisfied, and an automatic engine restart controller for automatically restarting the engine by causing the fuel injector of at least one of the cylinders (12A-12D) which is on expansion stroke at engine stop and causing the spark plug of that cylinder to ignite a mixture produced therein when predefined engine restart conditions are satisfied; characterized in that said automatic engine stop controller sets a scavenging mode period for expelling in-cylinder exhaust gas in an early part of automatic engine stop control operation, the scavenging mode period being a period during which the fuel injection from the fuel injectors is interrupted and the quantity of intake air regulated by said intake air quantity regulator is set at a level higher than a minimum quantity of intake air necessary for keeping the engine running by a specific amount and the amount of electric power generated by said alternator is decreased compared to the amount of electric power generated before fulfillment of the automatic engine stop conditions, said automatic engine stop controller causes said intake air quantity regulator to decrease the quantity of intake air and causes said alternator to increase the amount of electric power generated thereby at a point in time when the engine speed drops down to a predetermined reference engine speed after setting the scavenging mode period, and wherein, in executing the automatic engine stop control operation, said automatic engine stop controller detects the TDC engine speed at a point in time when a specific period of time has elapsed after the engine speed has dropped down to the predetermined reference engine speed and, based on the detected TDC engine speed, said automatic engine stop controller sets the amount of electric power to be generated by said alternator to adjust the rate of engine speed decrease such that the piston of at least one of the cylinders (12A-12D) which is on expansion stroke at engine stop stops within a specified range suited for engine restart, and whereby the range is defined by 100° to 120° after the compression stroke TDC in terms of crank angle.