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New observations of the swimming of several species of nereidiform polychaete are presented and the parameters of body motion analysed. It is shown that there are theoretical limits to the values of these parameters outside which propulsion by the wave motion of the body is impossible. Many of the observations do fall outside them. This is because of the effect of the beating parapodia. Kinematic considerations are introduced to show how the wave of parapodial activity is related to the wave motion of the body. Dynamic considerations lead to an estimate of the minimum Young's modulus of the parapodia for pure parapodial swimming, lower values being possible for a combination of body-wave and parapodial swimming. The speeds achieved by different methods of swimming are discussed for the species that have been examined.