The subject of this thesis is about the balancing of large flexible rotors which exhibit mixed modal characteristics. The objective of the research was to develop a balancing procedure to determine correction masses without trial runs. This required the determination of(a) the modal vibration vectors for each resonance, (b) the modal damping ratios,(c) the mode shapes and(d) the equivalent mass of the rotor for each mode. It was made clear from the beginning that trial runs are unavoidable either, when the mode shapes cannot be determined using an analytical or numerical method, or when there is dual vibration at normal operating speed, produced by the influence of higher unbalanced modes, is too high to allow continuous operation of the machine. Therefore, the scope of the project was limited to the possible determination of correction masses without trial runs for the vibration modes included within the normal operating range. Some studies about the minimisation or complete elimination of trial runs have been published by several authors, but a literature search revealed no reports of systematic application of these procedures to field balancing of large turbo generators. This suggested that some practical difficulties had still to be overcome, opening the possibility for further research on this area. Analysis of the rotor response demonstrated the necessity of considering the angular position of the transducers when registering the rotor vibration. It was shown that measuring in a direction other than those of the principal axes of stiffness introduces errors when determining the magnitude and phase of the correction masses. That is to say, failing to consider the effects of the transducer angular position eliminates the possibility of balancing the rotor without trial runs. This is the first time that this problem has been recognised. The procedure developed was verified using an experimental rotor rig. The successful application of the procedure to the balancing of this rotor demonstrates that balancing withouttrialrunsisnotonlyatheoreticalbutalsoapracticalpossibility. The dynamic characteristics of the rotor rig, however, were some what limited and did not cover all the possibilities considered during the project. Therefore, a more complete numerical example was also successfully solved using the computer model of a rotor with characteristics similar to those of a real turbine, and whose unbalanced distribution was not initially known by this author.