A process for operating a Coriolis mass flow rate measurement device, with at least one measurement tube (10) through which a medium flows and which is subjected to vibration excitation that leads to resulting vibrations of the measurement tube (10), a first indicator quantity being used for detection of a multiphase flow. For detection of the multiphase flow, an additional, second indicator quantity that is independent of the first indicator quantity is used. Thus, a process for operating a Coriolis mass flow rate measurement device (1) is attained with which the detection of multiphase flows, especially of two-phase flows, is reliably possible without the need to make assumptions regarding the properties of the individual phases of the flowing medium.