Dictyostelium development is based on cell-cell communication by propagating cAMP signals and cell movement in response to these signals.  In this paper we present a model describing wave propagation and cell movement during the early stages of Dictyostelium development, i.e. aggregation and mound formation.  We model cells as distinct units whose cAMP relay system is described by the Martiel-Goldbeter model.  To describe cell movement we single out three components: chemotactic motion, random motion and motion due to pressure between cells.  This pressure result in cells crawling on top of each other and therefore to the extension of the aggregate into the third dimension.  Using this model we are able to describe aggregation up to the mound stage.  The cells in the mound move in a rotational fashion and their movement is directed by the counter-rotating spiral of the chemo-attractant cAMP.  Furthermore, we show that the presence of two subpopulations with different inherent chemotactic velocities can lead to cell sorting in the mound.  The fast moving cells collect into the centre while the slow cells occupy the rest of the mound.  This model allows the direct comparison of the properties of the cAMP waves properties and movement behavior of individual cells with experimental data.  Thereby it allows a critical test of our understanding of the basic cellular principles involved in the morphogenesis of a simple eukaryote. Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited