Flowmeter for liquid/gas cryogenic two-phase fluids, comprising: - An inlet pipe for the fluid of which the flow rate is to be measured, in the flowmeter, which pipe is provided with a calibrated orifice; - A vertical reservoir, which reservoir is surrounded by an apparatus, into which reservoir said pipe opens, the wall of the reservoir being provided with a plurality of slots for outflow of the fluid forming a "spillway" system, from the reservoir towards the interior space inside the apparatus surrounding the reservoir; - Pressure sensors making it possible to measure the following pressure differences: • A pressure difference (ΔP3) between upstream and downstream of the calibrated orifice • A pressure difference (ΔP1) between the bottom of the reservoir and the atmosphere surrounding the reservoir within the interior space within the apparatus; • A pressure difference (ΔP2) existing between two points located in the space surrounding the reservoir within said interior space, making it possible to deduce the height of liquid downstream of the reservoir, in order to determine the state of the fluid, gaseous, two-phase or subcooled, and giving the level of liquid flooding downstream of the reservoir. - a data acquisition and processing system, which is able to carry out the following evaluations: a. determination of the information on the state of the incoming fluid: gaseous, two-phase or subcooled, from the pressure difference datum ΔP2; b. depending on this state information, the determination of said flow rate using either the pressure differential ΔP3 when the fluid is 100% gaseous or 100% liquid (subcooled), or the pressure differential ΔP1 that makes it possible to deduce the height of liquid in the reservoir and subsequently the flow rate of fluid passing through the slots. - An inlet pipe for the fluid of which the flow rate is to be measured, in the flowmeter, which pipe is provided with a calibrated orifice; - A vertical reservoir, which reservoir is surrounded by an apparatus, into which reservoir said pipe opens, the wall of the reservoir being provided with a plurality of slots for outflow of the fluid forming a "spillway" system, from the reservoir towards the interior space inside the apparatus surrounding the reservoir; - Pressure sensors making it possible to measure the following pressure differences: • A pressure difference (ΔP3) between upstream and downstream of the calibrated orifice • A pressure difference (ΔP1) between the bottom of the reservoir and the atmosphere surrounding the reservoir within the interior space within the apparatus; • A pressure difference (ΔP2) existing between two points located in the space surrounding the reservoir within said interior space, making it possible to deduce the height of liquid downstream of the reservoir, in order to determine the state of the fluid, gaseous, two-phase or subcooled, and giving the level of liquid flooding downstream of the reservoir. • A pressure difference (ΔP3) between upstream and downstream of the calibrated orifice • A pressure difference (ΔP1) between the bottom of the reservoir and the atmosphere surrounding the reservoir within the interior space within the apparatus; • A pressure difference (ΔP2) existing between two points located in the space surrounding the reservoir within said interior space, making it possible to deduce the height of liquid downstream of the reservoir, in order to determine the state of the fluid, gaseous, two-phase or subcooled, and giving the level of liquid flooding downstream of the reservoir. - a data acquisition and processing system, which is able to carry out the following evaluations: a. determination of the information on the state of the incoming fluid: gaseous, two-phase or subcooled, from the pressure difference datum ΔP2; b. depending on this state information, the determination of said flow rate using either the pressure differential ΔP3 when the fluid is 100% gaseous or 100% liquid (subcooled), or the pressure differential ΔP1 that makes it possible to deduce the height of liquid in the reservoir and subsequently the flow rate of fluid passing through the slots. a. determination of the information on the state of the incoming fluid: gaseous, two-phase or subcooled, from the pressure difference datum ΔP2; b. depending on this state information, the determination of said flow rate using either the pressure differential ΔP3 when the fluid is 100% gaseous or 100% liquid (subcooled), or the pressure differential ΔP1 that makes it possible to deduce the height of liquid in the reservoir and subsequently the flow rate of fluid passing through the slots.