Coriolis type flow measuring system for measuring the mass flow rate of a flowing medium, includes a flow tube and sensors associated with the flow tube for generating analog signals corresponding to the movement of the tube, analog to digital conversion elements for converting the analog sensor signals into digitized signals with a sampling frequency, and elements for calculating the mass flow rate from the digitized signals, which system is provided with members for causing the sampling of the sensor signals to take place with a number of different frequencies, elements for continuously measuring the rate at which the flow changes, and elements for selecting a predefined sampling frequency in dependence on the rate of change thus measured.