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Spanish bond yields, which posted their biggest one-day fall for two years on Monday on hopes of an end to political deadlock, fell a further 13 basis points on Tuesday to 1.33 percent.
Italian 10-year yields fell 8 bps to 1.35 percent but the gap between those and Spanish peers was at its tightest since July 2015.
Bond yields in peripheral eurozone states were dragged lower by expectations of further monetary easing by the European Central Bank to mitigate the fallout from last week's Brexit vote.