Disclosed is a device for the perfusion of an organ, including: a container of fluid, containing an organ bathed in the perfusion fluid; a first path including an inlet, an outlet and a pump; and a second path including an inlet, an outlet and a pump. The “arterial” outlet of the first path has a diameter smaller than a diameter of the “portal” outlet of the second path. The device additionally includes, between the pump and the outlet of the first path and/or between the pump and the outlet of the second path, an oxygenation unit arranged to oxygenate the fluid emerging from the “arterial” outlet of the first path more than the fluid emerging from the “portal” outlet of the second path. The device can include a communication path between the first path and the second path in order to oxygenate the second path. Use in liver transplantation.