The main purpose of this paper is to analyse the volatility spillovers in Latin American emerging stock markets. A multivariate Fractionally Integrated Asymmetric Power ARCH model with dynamic conditional correlations of Engle (1982) with a Student-t distribution is employed. We examine whether considering for long memory and asymmetry in emerging stock markets behaviour may provide more insights into the volatility spillovers phenomenon. In this paper we select daily frequency stock indexes covering four emerging countries in Latin America for the period (January 1995--September 2009). Our results point out the importance of volatility spillovers in these countries. Moreover, long memory and asymmetry in emerging stock market dynamics seem to provide more insights into the transmission of volatility shocks. More interestingly, the analysis of the DCCEs behaviour over time via multivariate cointegration, vector error correction model and the Cholesky variance decomposition shows shifts behaviour around major Latin American financial crisis and recent subprime crisis. On the practical side, these results may be useful for international portfolio managers and Latin American stock market authorities.