Spanish and Italian 10-year bond yields have been rising ahead of a summit of eurozone finance ministers on Monday.
The yield on Spanish 10-year bonds rose above 7% - a level considered to be unsustainable in the long term. Italian bond yields rose to 6.1%.
That's in stark contrast to the rates at a short-term German bond auction on Monday, where the yield on six-month bonds fell to a record low of -0.3%.
The BBC reports that means the investors are paying the German government to lend money to them.
It was the second time that German bond yields had been negative. The auction was oversubscribed, despite the negative yield.
France sold short-term bonds at negative yields for the first time on Monday.
Investors have been flocking to French and German debt as a safe haven from the problems elsewhere in the eurozone.