A fuel injection system for a spark-ignition internal combustion engine comprising: a number of cylinders, which receive a gas mixture comprising fresh air and wherein a plurality of respective main combustion chambers are defined; a number of first injectors, each coupled to a respective cylinder, into which it injects fuel under pressure during a combustion cycle; a number of spark plugs, each coupled to a respective cylinder to cyclically determine the ignition of the fuel present in the main combustion chamber; a number of combustion pre-chambers, each obtained in the area of a respective spark plug, where the combustion of a gas mixture comprising fresh air and fuel takes place in order to increase the turbulence inside the main combustion chamber of the respective cylinder; the injection system is characterized in that it comprises: a number of extraction ducts (17; 33), each originating from a respective cylinder in the area of an extraction point to extract the gas mixture present inside the respective main combustion chamber during a combustion cycle; at least one reserve, which receives the gas mixture from the extraction ducts (17; 28); inside the reserve, the gas mixture coming from the extraction ducts (17; 28) is mixed with the quantity of fuel needed to obtain a combustion under stoichiometric conditions inside the combustion pre-chambers; a number of second injectors, each coupled to a respective combustion pre-chamber, into which it injects the gas-and-fuel mixture coming from the reserve; and a third injector, which feeds the fuel to the reserve and is connected, by means of a first duct, to a low-pressure pump or, alternatively, to a high-pressure pump. a number of cylinders, which receive a gas mixture comprising fresh air and wherein a plurality of respective main combustion chambers are defined; a number of first injectors, each coupled to a respective cylinder, into which it injects fuel under pressure during a combustion cycle; a number of spark plugs, each coupled to a respective cylinder to cyclically determine the ignition of the fuel present in the main combustion chamber; a number of combustion pre-chambers, each obtained in the area of a respective spark plug, where the combustion of a gas mixture comprising fresh air and fuel takes place in order to increase the turbulence inside the main combustion chamber of the respective cylinder; the injection system is characterized in that it comprises: a number of extraction ducts (17; 33), each originating from a respective cylinder in the area of an extraction point to extract the gas mixture present inside the respective main combustion chamber during a combustion cycle; at least one reserve, which receives the gas mixture from the extraction ducts (17; 28); inside the reserve, the gas mixture coming from the extraction ducts (17; 28) is mixed with the quantity of fuel needed to obtain a combustion under stoichiometric conditions inside the combustion pre-chambers; a number of second injectors, each coupled to a respective combustion pre-chamber, into which it injects the gas-and-fuel mixture coming from the reserve; and a third injector, which feeds the fuel to the reserve and is connected, by means of a first duct, to a low-pressure pump or, alternatively, to a high-pressure pump. a number of extraction ducts (17; 33), each originating from a respective cylinder in the area of an extraction point to extract the gas mixture present inside the respective main combustion chamber during a combustion cycle; at least one reserve, which receives the gas mixture from the extraction ducts (17; 28); inside the reserve, the gas mixture coming from the extraction ducts (17; 28) is mixed with the quantity of fuel needed to obtain a combustion under stoichiometric conditions inside the combustion pre-chambers; a number of second injectors, each coupled to a respective combustion pre-chamber, into which it injects the gas-and-fuel mixture coming from the reserve; and a third injector, which feeds the fuel to the reserve and is connected, by means of a first duct, to a low-pressure pump or, alternatively, to a high-pressure pump.