Gaussian process models have some attractive advantages over parametric models and neural networks. They have a small number of tunable parameters, give a measure of the uncertainty of the model prediction, and obtain a relatively good model when only a small set of training data is available. In this study the theory of Gaussian process models has been applied to the neonatal seizure detection problem. Two measures are calculated from 1 second windows of EEG recordings; the variance (certainty) of a one step ahead prediction, and the ratio of the first model hyperparameter to the last. In ANOVA tests both measures show statistical difference in their values for non-seizure and seizure EEG. A comparison with a similar Autoregressive (AR) modelling approach shows that Gaussian Process model methods show great promise in real-time neonatal seizure detection.