The performance of a class of wave-power devices is studied theoretically by generalizing the known theory of ship dynamics with which there is good agreement with experiment. The extensions to the existing theory introduce the new features of asymmetry and articulation common to many proposed wave energy convertors. Results are presented for two different devices and a comparison is made between them. The performance calculations correlate very well with the available experimental evidence and moreover it would appear that the two types of device considered in this paper are comparable in their potential operating efficiencies if appropriate scales are chosen. The Salter duck and a two-pontoon system, semi-elliptical in cross section and hinged at its centre, constrained to move only in the mode in which energy is absorbed, appear to be equivalent. Both structures are designed such that when forced to move in their absorbing mode they generate waves in one preferred direction, the pontoon design relying on the use of a shallow horizontal breakwater in the rear of the moving structure whereas Salter has used a shorter deeper structure which looks almost cylindrical. When optimally loaded with a simple velocity-proportional damping applied externally, the performance of each system looks almost identical, with the pontoon being slightly better at the low frequency end. This parity is interesting and more general systems where the structures are free to move in many degrees of freedom must be examined. The reasons for this are apparent from calculated sea efficiencies of the devices. For the duck with a fixed centre and reactive loading, a 10 m diameter device may achieve an excellent performance over typical sea states, but if simple (velocity proportional) loading is used the diameter must increase to 15 m to give a comparable performance. If, however, the structure is free to move in other modes of motion with the same simple loading, then to achieve similar performance characteristics the structure has to be 30 m in diameter. Similar effects are found for the pontoon. Whereas an 80 m long two-pontoon system with a fixed rear section and simple loading will match to the sea conditions very well, a freely floating system with the same loading would need to be 120 m long to achieve a reasonable performance.