After-depolarisation is a hallmark of excitability in hippocampal pyramidal cells of CA1 and CA3 regions, because it constitutes the subthreshold relation between inward and outward ionic currents. This relationship determines the nominal response to stimuli and provides the necessary conditions for firing a spike or a burst of action potentials. Nevertheless, after-depolarisation is an inherently transient phenomenon that is not very well understood. We study after-depolarisation using a single-compartment pyramidal-cell model based on recent voltage-clamp and current-clamp experimental data. We systematically investigate CA1 and CA3 behaviour and show that changes to maximal conductance of T-type Ca2+- current, muscarinic-sensitive and delayed rectifier K+-currents are sufficient to switch the behaviour of the model from a CA3 to a CA1 neuron. We use model analysis to define after-depolarisation and bursting threshold. We also explain the influence of particular ionic currents on this phenomenon. This study ends with a sensitivity analysis that demonstrates the influence of specific currents on excitability. Counter-intuitively, we find that a decrease of Na+-current could cause an increase in excitability. Our analysis predicts that a change of high-voltage activated Ca2+- current can have a similar effect.