An exchange method for perfusion liquids for perfusing an organ through an ex vivo perfusion system; the ex vivo perfusion system comprising: - a container for an organ to be perfused, the container comprising a first reservoir initially containing a first perfusion liquid; - a perfusion circuit (39, 49, 50) fluidically connected to the first reservoir to perfuse the organ with the first perfusion liquid; - collection means (64, 71) configured to receive the first perfusion liquid at the end of the perfusion; and - a feed line (73, 75) designed to connect a second reservoir (72, 74) containing a second perfusion liquid different from the first perfusion liquid to the perfusion circuit (39,49, 50), wherein the feed line (73, 75) is provided with a valve designed to be opened and closed so as to allow the second perfusion liquid to be introduced into the perfusion circuit (39, 49, 50), the ex vivo perfusion system further comprising a thermoregulation system, coupled to a thermoregulation plate, and wherein the thermoregulation plate is adapted to carry the container and to rewarm or cool thanks to the thermoregulation system for rewarming or cooling the perfusion liquid contained in the container, wherein the method sequentially comprises the steps of: a) perfusing the organ with an initial amount of the first perfusion liquid by means of the perfusion circuit (39, 49, 50); b) during the perfusion of the organ with the first perfusion liquid, draining a first amount of the first perfusion liquid so as to reduce the amount of the first perfusion liquid in the perfusion circuit; c) during the perfusion of the organ with the first perfusion liquid, replacing the amount of the first perfusion liquid in the perfusion circuit with an equal amount of the second perfusion liquid; and d) continuing the perfusion of the organ with the second perfusion liquid, wherein, starting from step a), the temperature of the thermoregulation plate is gradually increased to pass from hypothermia to sub- and normothermia. the ex vivo perfusion system comprising: - a container for an organ to be perfused, the container comprising a first reservoir initially containing a first perfusion liquid; - a perfusion circuit (39, 49, 50) fluidically connected to the first reservoir to perfuse the organ with the first perfusion liquid; - collection means (64, 71) configured to receive the first perfusion liquid at the end of the perfusion; and - a feed line (73, 75) designed to connect a second reservoir (72, 74) containing a second perfusion liquid different from the first perfusion liquid to the perfusion circuit (39,49, 50), - a container for an organ to be perfused, the container comprising a first reservoir initially containing a first perfusion liquid; - a perfusion circuit (39, 49, 50) fluidically connected to the first reservoir to perfuse the organ with the first perfusion liquid; - collection means (64, 71) configured to receive the first perfusion liquid at the end of the perfusion; and - a feed line (73, 75) designed to connect a second reservoir (72, 74) containing a second perfusion liquid different from the first perfusion liquid to the perfusion circuit (39,49, 50), wherein the feed line (73, 75) is provided with a valve designed to be opened and closed so as to allow the second perfusion liquid to be introduced into the perfusion circuit (39, 49, 50), the ex vivo perfusion system further comprising a thermoregulation system, coupled to a thermoregulation plate, and wherein the thermoregulation plate is adapted to carry the container and to rewarm or cool thanks to the thermoregulation system for rewarming or cooling the perfusion liquid contained in the container, wherein the method sequentially comprises the steps of: a) perfusing the organ with an initial amount of the first perfusion liquid by means of the perfusion circuit (39, 49, 50); b) during the perfusion of the organ with the first perfusion liquid, draining a first amount of the first perfusion liquid so as to reduce the amount of the first perfusion liquid in the perfusion circuit; c) during the perfusion of the organ with the first perfusion liquid, replacing the amount of the first perfusion liquid in the perfusion circuit with an equal amount of the second perfusion liquid; and d) continuing the perfusion of the organ with the second perfusion liquid, a) perfusing the organ with an initial amount of the first perfusion liquid by means of the perfusion circuit (39, 49, 50); b) during the perfusion of the organ with the first perfusion liquid, draining a first amount of the first perfusion liquid so as to reduce the amount of the first perfusion liquid in the perfusion circuit; c) during the perfusion of the organ with the first perfusion liquid, replacing the amount of the first perfusion liquid in the perfusion circuit with an equal amount of the second perfusion liquid; and d) continuing the perfusion of the organ with the second perfusion liquid, wherein, starting from step a), the temperature of the thermoregulation plate is gradually increased to pass from hypothermia to sub- and normothermia.