A ship's propulsion system (1; 1'), comprising: a driveshafting (10; 10') having a propeller shaft (15, 15'), which is equipped to receive torsional drive power from an internal combustion engine and feed torsional drive power to a propulsion element, a first clutch with a clutch input and a clutch output, which can be selectively connected and drive disconnected to one another, wherein the clutch input of the first clutch is drive-connected to the driveshafting (10; 10'), so that torsional drive power can be transmitted to the propulsion element, a first transmission with two transmission interfaces (41, 43), via which torsional drive power can be fed to and removed from the first transmission in each case, wherein a first transmission interface of the first transmission is drive-connected to the clutch output of the first clutch, and wherein the internal combustion engine drives into a second transmission interface of the first transmission, an elastically mounted second transmission with a transmission input and a transmission output, which is drive-connected to the driveshafting (10; 10'), wherein the transmission output of the second transmission is drive-connected to the driveshafting (10; 10') via cardanic coupling means (55, 55') allowing axial and angular and radial offsets, and wherein the second transmission from its transmission input to its transmission output provide a rotational speed reduction, a fast-running electric motor which is equipped in order to feed torsional drive power to the driveshafting (10; 10') via the transmission input of the second transmission, and a second clutch (70, 65') with a clutch input and a clutch output which can be selectively drive-connected and disconnected to/from one another in order to establish or disconnect a drive connection of the electric motor with the clutch input of the first clutch. a driveshafting (10; 10') having a propeller shaft (15, 15'), which is equipped to receive torsional drive power from an internal combustion engine and feed torsional drive power to a propulsion element, a first clutch with a clutch input and a clutch output, which can be selectively connected and drive disconnected to one another, wherein the clutch input of the first clutch is drive-connected to the driveshafting (10; 10'), so that torsional drive power can be transmitted to the propulsion element, a first transmission with two transmission interfaces (41, 43), via which torsional drive power can be fed to and removed from the first transmission in each case, wherein a first transmission interface of the first transmission is drive-connected to the clutch output of the first clutch, and wherein the internal combustion engine drives into a second transmission interface of the first transmission, an elastically mounted second transmission with a transmission input and a transmission output, which is drive-connected to the driveshafting (10; 10'), wherein the transmission output of the second transmission is drive-connected to the driveshafting (10; 10') via cardanic coupling means (55, 55') allowing axial and angular and radial offsets, and wherein the second transmission from its transmission input to its transmission output provide a rotational speed reduction, a fast-running electric motor which is equipped in order to feed torsional drive power to the driveshafting (10; 10') via the transmission input of the second transmission, and a second clutch (70, 65') with a clutch input and a clutch output which can be selectively drive-connected and disconnected to/from one another in order to establish or disconnect a drive connection of the electric motor with the clutch input of the first clutch.