Abstract: A method and Coriolis mass flowmeter, wherein the Coriolis mass flowmeter includes at least one measurement tube through which a medium flows, at least one exciter system arranged in the central region of the at least one measurement tube which causes the measurement tube to oscillate, and at least two oscillation pick-ups arranged in front of and behind the at least one exciter system. The at least two measurement tubes are additionally each provided with at least one acceleration sensor arranged in front and/or behind the exciter system. An evaluation device is configured to receive acceleration signals from the acceleration sensors and evaluate the acceleration signals to diagnose an asymmetry in the measurement tubes such that fault states, such as deposits in one of the two measurement tubes, blockage of a tube in a flow divider or asymmetrical changes in the ability of the measurement tubes to oscillate, such as due to cracks or fractures, can advantageously be detected.