This paper examines carbon price volatility using data from the European Union Emission Trading Scheme from a nonlinear dynamics point of view. First, we use a random walk model, including serial correlation and variance ratio tests, to determine whether carbon price history information is fully reflected in current carbon price. The empirical research results show that carbon price is not a random walk: the price history information is not fully reflected in current carbon price. Second, use R/S, modified R/S and ARFIMA to analyse the memory of carbon price history. For the period April 2005-December 2008, the modified Hurst index of the carbon price is 0.4859 and the d value of ARFIMA is -0.1191, indicating short-term memory of the carbon price. Third, we use chaos theory to analyse the influence of the carbon market internal mechanism on carbon price, i.e., the market's positive and negative feedback mechanism and the heterogeneous environment. Chaos theory proves that the correlation dimension of carbon price increases. The maximal Lyapunov exponent is positive and large. There is no obvious complex endogenous phenomenon of nonlinear dynamics the carbon price fluctuation. The carbon market is mildly chaotic, showing both market and fractal market characteristics. Price fluctuation is not only influenced by the internal market mechanism, but is also impacted by the heterogeneous environment. Finally, we provide suggestions for regulation and development of carbon market. (C) 2010 Published by Elsevier Ltd.