We analyse the links between credit default swap (CDS) and bond spreads in order to determine which one is the leading market in the price discovery process. To do that, we construct a sample of CDS premia and bond spreads on a generic 5‐year bond for 17 financials and 18 sovereigns. First, we run panel vector error correction model estimations, showing that the CDS market has a lead over the bond market for financial institutions. This also holds for high‐yield sovereigns, whereas the reverse is found for low‐yield sovereigns in the core of the euro area. We interpret these results according to the relative liquidity of both markets for different types of entities. Second, we check for nonlinearities in the adjustment process. Results show that the CDS market's lead is amplified when default risk increases, during crisis periods, as well as continuously when CDS premia increase.