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Data compression deals with removal of redundancy, reducing bandwidth and thus lowering transmission and storage costs. Telemetry data can be sensitive to inaccuracies and require lossless compression for exact reconstruction at the receiver. One technology that has been successfully applied in a wide range of applications is artificial neural networks (ANN), a massively parallel system with pattern recognition capabilities. This monograph is a reproduction of the author s postgraduate thesis work at Multimedia University, Malaysia. A two-stage predictor-encoder combination is proposed, incorporating a variety of feedforward, recurrent and radial basis ANN architectures, as the predictors. The encoders are well known compression algorithms. Characteristic features of the models, transmission issues and other practical considerations are taken into account to determine optimised configuration of the schemes. Significant compression results are reported, along with a critical review of the strengths and weaknesses of over 50 implementations simulated with satellite telemetry data.