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Coriolis mass flowmeters (CMF) are direct mass flowmeters and form a real mean along the flow profile. They do not exploit secondary physical properties of the specific liquid, such as fluid velocity and fluid density in the measuring process, but directly exploit the primary property inertia to measure mass flow. However, there is some evidence from field applications that the devices, in particular those using a single straight pipe, suffer from parameter variation. Therefore, the flowmeter has to be carefully adjusted with respect to physical properties of the liquid, operating conditions, and site installation. When modeling the CMF using two oscillatory systems referring to the first and second mode, the mass flow enforces the coupling of these oscillatory systems. In the ideal case, the coupling is only affected by the mass flow. Detailed analysis, however, reveals that asymmetries in installation, sensors, actuators, as well as pipe-inhomogeneities heavily contribute to this coupling and thus lead to a parameter variation. In this paper, a model-based approach is presented to identify the parameters of the model using an auxiliary excitation of the system.