In this globalized world, market efficiency is one of the main determinants of country positions in the international economic and financial space. Aware of this crucial issue, this article aims to provide further evidence on the weak form of the Efficiency Hypothesis in Sovereign CDS markets in 37 countries around the world from January 2006 to March 2017. The econometric framework used in this research is based on a VECM-FIGARCH(1,d,1) approach that considers for long term equilibrium as well as volatility stylized facts such as clustering and long-memory. Based on the entire period analysis and against all odds, the results clearly reject the randomness of each CDS spread studied. However, the sub-period analysis shows significant evidence of structural breaks in the price predictability pattern, characterized by some efficiency decline over the last two financial tensions. The significant impact of crises on market efficiency is all the more justified because, during the post-crisis period, historical prices are found to be completely irrelevant in predicting current spreads. Moreover, our results show that each country of the economically heterogeneous studied sample exhibit different efficiency status that cannot be adequately explained by the sovereign credit risk level. JEL Classification: G01, G14