A method for operating a Coriolis mass flowmeter that has at least one measuring tube with medium flowing through it involves exciting the measuring tube excited to oscillation, detecting the oscillations of the measuring tube and determining the density of the medium. Detection of the state and a change in the state of a Coriolis mass flowmeter is achieved by determining a calibration temperature and a calibration density sensitivity of the Coriolis mass flowmeter using the detected oscillations, at a temperature differing from the calibration temperature, and a density sensitivity of the flowmeter determined using the detected oscillations. A measurement rate of change of the density sensitivity is determined and a forecast rate of change of the density sensitivity is calculated using a forecast algorithm, and at a given deviation of the measurement rate of change from the forecast rate of change rp, a deviation signal is generated.