Several researchers propose that event-related potentials (ERPs) can be explained by a superposition of transient oscillations at certain frequency bands in response to external or internal events. The transient nature of the ERP is more suitable to be modelled as a sum of damped sinusoids. These damped sinusoids can be completely characterized by four sets of parameters, namely the amplitude, the damping coefficient, the phase and the frequency. The Prony method is used to estimate these parameters. In this study, the long-latency auditory-evoked potentials (AEP) and the auditory oddball responses (P300) of 10 healthy subjects are analysed by this method. It is shown that the original waveforms can be reconstructed by summing a small number of damped sinusoids. This allows for a parsimonious representation of the ERPs. Furthermore, the method shows that the oddball target responses contain higher amplitude, slower delta and slower damped theta components than those of the AEPs. With this technique, we show that the differentiation of sensory and cognitive potentials are not inherent in their overall frequency content but in their frequency components at certain bands.