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Prediction plays a key role in many signal processing applications. Linear Prediction has, in particular, been extremely useful to the development of digital speech processing techniques and applications. There is however a growing need for improved forms of prediction. We discuss, in this paper, a form of non-linear prediction, namely, the prediction of the phase of speech signals. This study is conducted within a short-time analysis/synthesis framework and is based upon a new treatment of the classical speech production model. Experimental data are presented confirming the theoretical results. Finally the use of phase prediction to low-bit rate, high-quality coding applications is discussed.