A measuring system for measuring a mass flow rate, a density, a temperature or a flow velocity. The measuring system includes a main line, a first Coriolis measuring device arranged in the main line, a second Coriolis measuring device arranged in series with the first Coriolis measuring device in the main line, a bypass line which bypasses the second Coriolis measuring device, a first valve arranged in the bypass line, and a computing unit which is connected to the first Coriolis measuring device and to the second Coriolis measuring device. The first valve opens depending on a pressure. The first Coriolis measuring device is designed for a higher maximum flow rate than the second Coriolis measuring device.