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Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet, an increasing interest for a comprehensive model for movement generation requires to bridge the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movement within the framework of motor primitives, i.e. of modular generation of movements. Thereby we hope to get an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed relatively to biological concepts such as force fields and central pattern generators and are then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes this work.