An oil supply system for an internal combustion engine includes an oil pump, a heat exchanger, an oil feed line and two oil outlet lines, for conveying the oil from the oil pump through the oil feed line to the heat exchanger and from the latter through the two oil outlet lines. In a system of this type, there is provision for the internal combustion engine to be configured as a piston engine and for the heat exchanger to be configured as a water/oil heat exchanger, and for one oil outlet line to be connected to oil spray nozzles of the piston engine and for the other oil outlet line to be connected to a main oil line of the piston engine. An oil supply system of this type is distinguished by its simple design and functionality, and permits optimum cooling and lubrication of the relevant components of the engine.