A process for operating a Coriolis mass flow rate measurement device which has at least one measurement tube, the measurement tube being excited into vibrations with a predetermined excitation frequency and a predetermined excitation phase. The response phase which is achieved thereby and the rate of change of the response phase are detected and the excitation frequency is changed by the frequency amount which arises based on a predetermined function from the detected rate of change of the response phase. This makes it possible to maintain continuous measurement of the mass rate of flow even if two-phase flows occur.