We have studied optical density wave propagation during aggregation of the cellular slime mould Dictyostelium discoideum in a quantitative manner by digital image analysis. The waves are mostly single ended spiral waves starting from an aggregation center. We can measure a variety of parameters such as oscillation frequency, wave propagation velocity and wave shape. This allows the construction of dispersion curves under a variety of experimental conditions. During later development where the optical density waves are no longer visible we have started to measure movement of fluorescently labelled cells. Our main conclusions from these measurements are that the cells continue to move chemotactically to periodic signlas both in aggregates and in slugs. There is a dramatic difference in the movement pattern of prestalk and prespore cells: Prestalk cells move perpendicular to the long axis of the slug, they are most likely organized by a scroll wave. Prespore cells seem to move almost perpendicular to the prestalk cells, in the direction of the tip. This behaviour is explained on the basis of different relay properties of prespore and prestalk cells.