In the international oil and gas industry multiphase annular flow in pipelines and wells is extremely important, but not well understood. This thesis reports the development of an efficient and cheap method for measuring the phase flow rates in two phase annular and annular mist flow, in which the liquid phase is electrically conducting, using ultrasonic and conductance techniques. The method measures changes in the conductance of the liquid film formed during annular flow and uses these to calculate the volumetric and mass flow rates of the liquid film. The gas velocity in the core of the annular flow is measured using an ultrasonic technique. Combined with an entrainment model and the liquid film measurements described above, the ultrasonic technique enables the volumetric flow rate of the gas in the core and the volumetric and mass flow rates of entrained liquid droplets to be measured. This study was based on experimental work and the use of modelling techniques. The practical investigation comprised a series of experiments conducted on a purpose built flow loop in which the test section was a Perspex pipe of 50mm ID. The experimental work was limited to two-phase air-water flow. The flow loop was specifically designed to accommodate the different instruments and subsystems designed in this investigation including bespoke flow meters and a film extraction system. Most flow loop controls were automated using a MATLAB program. Reference measurement of the total water flow rate was made using a calibrated turbine flow meter and of the air flow rate using a calibrated rotameter. For the combined ultrasonic/conductance method investigated in this thesis, the velocity of the gas in the core was found using a novel Ultrasonic Flow Meter (USFM). The positioning and arrangement of the transducers have never been used previously. The flow velocity of the liquid film and the thickness of the film were measured using a novel Conductance Flow Meter (CFM). The CFM measured the liquid film thickness using novel wall conductance probes. By cross correlating the signals from a pair of such probes the film velocity was obtained. Good agreement of the experimental results obtained from the CFM and USFM with results published in the literature was found. Although not investigated experimentally in the work described in this thesis, annular flows encountered in the oil industry may contain a liquid phase comprising a mixture of oil and water. For such flows, the volume fractions of the oil and water can be measured using an automated bypass system developed during this project. The bypass system periodically extracts part of the liquid film, measures its density and then releases the sample back into the pipeline. The liquid phase volume fractions are determined from this density measurement which can be performed more than once per minute. An entrainment model was developed, which is required by the ultrasonic/conductance flow metering technique described in this thesis, in which the mass fraction of the liquid flowing as entrained droplets in the core can be determined from the liquid film thickness and velocity measurements. A mathematical model was also developed to describe the properties of the liquid film, such as liquid velocity profile within the film, and the model?s results were found to agree with the experimental results obtained during the project and also with previous work cited in the literature. The complexity of this latter model was reduced by making a number of simplifying assumptions, which are presented and discussed in the thesis, including the assumption that in annular flow there is a dynamic balance liquid entrainment and droplets being deposited back onto the film. The combination of the designed CFM and USFM with the bypass tube and the entrainment model offer the opportunity for a?wet gas? flow meter to be developed to measure two and three phase annular flows at relatively low cost and with enhanced accuracy. Such a device would have the advantage that it would by substantially smaller than systems using separators and it could even be retrofitted onto off-shore platforms. The integration of the subsystems developed in this project into a single system capable of giving on-line measurements of annular flow would be a major benefit to the author?s sponsor, Petroleum Development of Oman.