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Purpose – This paper aims to examine the dynamic relationship across stock market returns in Morocco, Tunisia, Egypt, Lebanon, Jordan, Kuwait, Bahrain, Qatar, United Arabic Emirates (UAE), Saudi Arabia, and Oman from June 2005 to January 2012. Design/methodology/approach – The paper uses a multivariate model with leptokurtic distribution which allows for both return asymmetry and fat tails. The paper also derives from the model the conditional correlation between stock markets and examines the impact of the global financial crisis of 2008 on the conditional variance and correlation. Findings – The empirical results show that the Middle East and North African (MENA) markets are interconnected by their volatilities and not by their returns. Volatility persists in each market and significant volatility spillovers from small to relatively larger markets. During the crisis, the paper finds that conditional volatilities across markets increase but then during the post-crisis period return to their pre-crisis levels. More importantly, the conditional correlation behaves differently, with a significant evidence of downwards trend in some correlations across the MENA stock markets. Research limitations/implications – One limitation of the study relates to the relatively short-sample period which drives the empirical results. Practical implications – The key results imply that there is still a possibility of benefits from portfolio diversification across specific MENA countries during periods of high volatility. Originality/value – No previous study investigates the transmission of both the first and second moments of the return series across the MENA stock markets allowing for time-varying volatility and correlation and accounts for the 2008 global financial crisis to examine whether the conditional volatilities and correlations have strengthened or weakened during the crisis and afterwards. [ABSTRACT FROM AUTHOR]