An architecture of a propulsion system of a multi-engine helicopter is disclosed, comprising turboshaft engines that are connected to a power transmission gearbox. It comprises: a hybrid turboshaft engine that is capable of operating in at least one standby mode during a stable flight of the helicopter; a pack for quickly restarting said hybrid turboshaft engine in order to bring said engine out of said standby mode and to reach a nominal operating mode; an auxiliary power unit that is connected to said electrotechnical restart pack by means of a first AC/DC converter and is capable of providing said restart pack, on demand, with power required for bringing said hybrid turboshaft engine out of said standby mode.