In the first few hours after starvation, the developing cAMP secretory system in Dictyostelium discoideum has been observed to be successively in one of four states: (a) quiescent, (b) excitable (capable of relay), (c) autonomously oscillating, and (d) secreting at a high steady level. A theoretical model is presented which demonstrates that the proximal cause of the transitions between different types of behavior may be slow changes in the activities of the enzymes adenylate cyclase and phosphodiesterase. These changes affect the stability properties of the steady state admitted by the cAMP signalling system. Sustained oscillations develop when the steady state is unstable, whereas relay of cAMP signals occurs upon perturbation of a stable steady state for parameter values close to those which produce oscillations. The developmental path suggested in the adenylate cyclase-phosphodiesterase space for the sequential transitions compares with the time course observed for the synthesis of these enzymes after starvation. It is suggested that there is general significance for the understanding of differentiation in the example given of a state-point following a developmental path in parameter space, moving from one behavioral domain to another, and thereby bringing about shifts in qualitative behavior.