This study examines for the first time the relationship among the oil price shocks and the sovereign yield spreads in the EMU (which is collectively the largest oil-importer of the world), in a time-varying environment. In particular, we examine the time-varying correlation between oil price shocks and the 10-year sovereign yield spread of core and periphery countries in the EMU, by employing a scalar-BEKK framework. The main findings reveal that the correlations between sovereign yield spreads and oil price shocks are indeed time-varying and are influenced by specific economic and geopolitical events that took place during the study period. Furthermore, even though the correlation patterns are constantly low or zero prior to the Great Recession, a change is revealed in the post-2008 period, when correlations become moderate and more volatile. Finally, we do not observe noteworthy differences in the correlation behaviour between core and periphery countries to different oil price shocks. The findings of this study are particularly useful and provide valuable information to marketplace participants. •We assess the time-varying relationship between the oil price shocks and the 10-year sovereign yield spreads.•We focus on the European Monetary Union, which is the largest oil-importer of the world.•We show that the relationship is influenced by specific economic and geopolitical events.•Correlations are heterogenous depending on the oil price shock.•We do not find noteworthy differences in the correlation behaviour among core and periphery EMU countries.