The low oil price recently has caused fears about the sustainability of public finances in some oil producing countries. We examine the relationship between oil prices and sovereign credit risk examining the CDS market. Analysing data from nine countries (Brazil, Malaysia, Norway, Qatar, Russia, Saudi Arabia, the United Kingdom, the United States of America and Venezuela) we have estimated bivariate VAR-GARCH-in-mean models. The results of our empirical investigations generally speaking do suggest that positive oil price shocks lead to lower sovereign CDS spreads. Thus, our findings support the hypothesis that higher oil prices improve the fiscal stability of oil producing countries.