A fuel system (10) for supplying fuel (18) to an internal combustion engine, with a reservoir (16), a first fuel pump (20) whose input is connected to the reservoir (16), a second fuel pump (38) whose input is connected to the first fuel pump (20), at least one injection valve (50), which is connected to the second fuel pump (38) and can supply fuel (18) at least indirectly into a combustion chamber, and a leakage line provided between the second fuel pump and the reservoir, characterized in that the leakage line (68) contains a valve device (70), with a shutoff function (72) and a pressure relief function (74) that are connected in parallel with each other.