Coriolis Mass Flowmeters are widely used for industrial flOW' measurements due to their high performance in the mass flow rate metering of single-phase fluids, However, the accuracy of the meters degrades when bubbly or particulate two-phase flows are measured.In this work, the mechanisms leading to this performance degradation are investigated. The theory describing the moving resonator effect ia developed to explain the measurement errors caused by the compressibility of the bubbly two-phase fluid. Therefore, the complex behavior of the two-phase fluid in the messuring tube of a Coriolis mass flow meter is simulated by a moving resonator model. With the help of this simple model, the measurement errors of the Coriolis mass flowmeter due to the compressibility of the two-phase fluid can be quantitatively estimated.The above theory, in combination with the existing bubble theory, forms the theoretical basis of the compensation for Coriolis bubbly or particulate flow measurements.Two compensazion schemes, the two-mode compensation scheme and the CMF-damping compensation scheme, are then proposed to eliminate the influence of the moving resonator effect and the bubble effect on the measurements of Coriolis mass flowmeters. As a part of this research, the above two compensation schemes are validated by experiments carried out with various bubbly two- phase flows of different fluids and flow patterns.