Gaussian process (GP) probabilistic models have attractive advantages over parametric and neural network modeling approaches. They have a small number of tuneable parameters, can be trained on relatively small training sets, and provide a measure of prediction certainty. In this paper, these properties are exploited to develop two methods of highlighting the presence of neonatal seizures from electroencephalograph (EEG) signals. In the first method, the certainty of the GP model prediction is used to indicate the presence of seizures. In the second approach, the hyperparameters of the GP model are used. Tests are carried out with a feature set of ten EEG measures developed from various signal processing techniques. Features are evaluated using a neural network classifier on 51 h of real neonatal EEG. The GP measures, in particular, the prediction certainty approach, produce a high level of performance compared to other modeling methods and methods currently in clinical use for EEG analysis, indicating that they are an important and useful tool for the real-time detection of neonatal seizures.