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Lossless compression of electroencephalograph (EEG) data is of great interest to the biomedical research community. Lossless compression through neural network is achieved by using the net as a predictor and coding the prediction error in a lossless manner. The predictive neural network uses a certain number of past samples to predict the present one and in most cases, the differences between the actual and predicted values are zero or close to zero. Entropy coding techniques such as Huffman and arithmetic coding are used in the second stage to achieve a high degree of compression. Predictive coding schemes based on single- layer and multi-layer perceptron networks and recurrent network models are investigated in this paper. Compression results are reported for EEG's recorded under various clinical conditions. These results are compared with those obtained by using linear predictors such as FIR and lattice filters.