Mathematical models of biological processes which have been observed in vivo to be highly robust to intracellular and environmental variations should themselves display appropriate levels of robustness when analysed in silico. This paper uses techniques from robust control theory to analyse and extend a mathematical model of the interacting proteins underlying adenosine 3′, 5′-cyclic monophosphate (cAMP) oscillations in aggregating Dictyostelium cells. Starting with a previously proposed ‘minimal’ model, we show how robustness analysis using the structured singular value can identify points of structural fragility in the network. By combining these results with insights from recent results from the experimental literature, we show how the original model can be augmented with some important additional modules, comprising networks involving IP3 and Ca2+. By analysing the robustness of our new extended model, we are able to show that dynamic interactions between the different modules play a pivotal role in generating robust cAMP oscillations; thus, significantly improving our understanding of the design principles underlying this complex biological system. Copyright © 2009 John Wiley & Sons, Ltd.