This paper has two objectives. First, we apply the symmetric and asymmetric VAR(1)-BEKK-MGARCH(1.1), VAR(1)-CCC-MGARCH(1,1), VAR(1)-DCC-MGARCH, VAR(1)-VARMA-CCC-MGARCH and VAR(1)- VARMA-DCC-MGARCH models to explore the return and volatility interactions among electricity and other fuel price markets(oil, natural gas, and coal). Second, this paper investigates the importance of not only volatility spillover among energy markets, but also the asymmetric effects of negative and positive shockson the conditional variance of modeling one energy market’s volatility upon the returns of future prices within and across other energy markets. The empirical results display that these models do capture the dynamic structure of the return interactions and volatility spillovers and exhibit statistical significance for own past mean and volatility short-and long-run persistence effects, while there are just a few cross-market effects for each model.