We argue that a "static" specification of the Maastricht criterion for long-term bond yields is not conducive to assessing stability of financial systems in euro-candidate countries. Instead, we advocate a dynamic approach to assessing interest rate convergence to a common currency that is based on the analysis of financial system stability. Accordingly, we empirically test volatility dynamics of the ten-year sovereign bond yields of the 2004 EU accession countries in relation to the eurozone yields during the January 2, 2001-January 22, 2009, sample period. Our results show a varied degree of the relationship between domestic and eurozone sovereign bond yields, the most pronounced for the Czech Republic, Slovenia, and Poland, and weaker for Hungary and Slovakia. We find some divergence of relative bond yields since the EU accession.