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This paper presents a new technique to detect P300 peaks in continuous EEG recordings using a spiking neural network model. Human EEG signals recorded during spell checking, downloaded from the BCI Competition website, were pre-processed using a Wavelet Transform to remove the noise and to extract the low frequency content of the signal. Analysis of the signals was performed on the ensemble EEG and the task of the neural network was to identify peaks of different shapes. The network has a time-warp invariance property, which means that an input linearly compressed or elongated in time is still recognisable by the network. This enabled the network to train on one peak shape and generalize it to recognise similarly shaped peaks. The neural network presented was trained on one epoch of filtered EEG and was tested on the remaining samples. 94.7% of the signals assigned as containing P300 by the paradigm used for the data on the website were correctly classified as P300s, and 83.7% of the non-P300s were also classified as non-P300s. The sensitivity of the technique, utilising the data from this paradigm was 94.7%, specificity 69.5%, and positive predictive value was 38.29%.