We analyze time-variation of the price discovery process in sovereign debt markets. We test whether the cointegrating relationship that should tie bond and CDS spreads together holds. In addition, we investigate which (if any) of the two markets leads price discovery in a number of sub-samples. We focus on ten Eurozone countries, the UK, and the US. While for all the peripheral countries but Greece CDS and bond spreads show a long-run equilibrium relationship, this is not the case for core European countries, the UK, and the US. When cointegration fails to hold, none of the markets leads price discovery.