The behaviour of Dictyostelium discoideum amoebae has been studied in natural cAMP waves and in controlled spatial and temporal gradients. Chemoattractant gradients induce responses which indicate that amoebae spatially compare concentration increases at different points on the cell surface. This allows them to respond to the relative spatial and temporal gradients in a manner that is little affected by the absolute attractant concentration over several orders of magnitude. The changes in turning behaviour, motility and morphology that are induced by attractant gradients are consistent with transduction of stimuli into two intracellular signals - one activating and the other inhibiting pseudopodium formation. The former measures the present attractant concentration at particular points on the cell surface - the local, current signal. The latter measures the average attractant concentration over the whole cell surface during the recent past - the global, past signal. Both signals may be part of a normal pseudopodium autoactivation and inhibition system responsible for amoeboid morphology and motility. Attractants could modulate this system to generate the complex behavioural responses observed.