This paper examines the correlation estimates for some East Asia equity markets using the CC-MGARCH and DCC-MGARCH. Using daily return series, the equity markets of Korea, Japan, Hong Kong, and Singapore are analysed for the period 1991 to 2005. Parsimonious specifications for the multivariate GARCH framework are used to shed light on the correlation structure of these markets. The dynamic nature of the correlation between pair-wise countries is captured using the dynamic conditional correlation multivariate GARCH framework and explained. First, there are no strong evidence of time-varying correlations for the sample period. However, there are weak evidence of time-varying correlation between some countries in post-crisis period. Second, the correlation breakdowns are occurred between Korea and other countries about the time of the Asian financial crisis, but it do not appear in the case of other countries. Third, the correlation generally has a property of long-run persistence, but the degree of persistence are much weakened between countries except Korea in post-crisis period. Finally, the local extreme shock affects correlation, and there is also a evidence of correlation asymmetry. Namely, the effect of negative extreme shocks are more stronger than that of positive extreme shocks.