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Compression of EEG signals have a basic role in the consumption power reduction of an ambulatory EEG system. This paper outlines a scheme for EEG compression based on adaptive model arithmetic coding (AMAC) and First order Markov (FM) model. In this scheme, signals are stored within an L-second buffer and quantized to some levels. Then, the AMAC-FM compression algorithm is applied to encode the symbols sequence for wireless transmission. In order to achieve the optimal entropy, this algorithm changes dynamically probability distribution of symbols based on current encoded symbols between encoder and decoder. Finally, the proposed algorithm is established to compression of Freiburg University epilepsy EEG dataset and compression ratio (CR) is obtained. The results indicate that our algorithm can achieve a high CR in relation to other EEG compression methods such as JPEG2000.