A system supplies gas to a high-pressure gas-consuming apparatus and a low-pressure gas-consuming apparatus of a floating structure including a tank. The supply system includes: a first supply circuit, a second supply circuit, a return line, a first heat exchanger and a second heat exchanger. The return line includes a flow-regulating member. The supply system includes a device for managing the supply system which includes a control module to control the flow-regulating member based on the characteristics of the gas.