This study investigates how differently have the CDS spreads of EMU core, EMU periphery, and non-EMU economies evolved in the progress of the Global Financial Crisis (GFC) and the Eurozone Debt Crisis (EDC). We employ AR-X-GARCH-copula models to analyze the heterogeneous patterns in the movements of the CDS spreads across the three groups and two crises. We find that the value of EUR among the common determinants has asymmetric effect on the EMU periphery group and the others. Furthermore, only Greece and Ireland experiences structural changes in the conditional means after controlling for the common determinants. In terms of conditional volatility, the three groups exhibit similar structural increases during the GFC, however, the EMU periphery group shows obviously larger increment than the others in the EDC period. As a result of the dependence analysis, we find (EMU core, EMU core) and (non-EMU, non-EMU) pairs generally experience structural increase in both the Gaussian and tail dependences during the two crises. However, (EMU periphery, EMU periphery) overall exhibits no or structural decrease in dependence. Lastly, the asymmetry in dependence becomes more skewed to the lower tail for the GFC period whereas it stays similar for the EDC period, in general.