Oscillating bodies constitute a major class of wave energy converters, especially for offshore deployment. In general, such converters use as power take-off system either a hydraulic system (high-head water turbine or high-pressure-oil hydraulic motor) or a directly driven linear electric generator. The paper addresses the former case, especially when a gas accumulator is employed as energy storage device that provides a smoothing effect to the electric power output. Although there are several wave energy projects currently at different stages of development (including prototype testing) that fit this description, the paper is intended to be a general modelling study rather than to concentrate on a particular device. Special attention is devoted to power take-off performance and design, and to the control of the system.