A fuel injection system for internal combustion engines is proposed, in which with the aid of a high-pressure pump fuel is pumped at high pressure into a high-pressure fuel reservoir (6), from which electrically controlled fuel injection valves (9) are supplied. The pressure in the high-pressure fuel reservoir is maintained in such a way that a first pump element (16) pumps fuel into the high-pressure reservoir with a variable pumping quantity, and a second pump element (17) as needed pumps a constant high-pressure fuel quantity into the high-pressure reservoir. A simple, economical system is thus obtained for furnishing high fuel pressure for injection by the fuel injection system (FIG. 2).