Arwel Jones from the National Library of Wales told ITV News that he is hoping that the damage will be limited - "the most valuable stuff is housed in purpose-built cells at the very bottom of the library, and this fire is at the very top."
He admitted to concern that the damage from water pumped onto the building by firefighters would be as bad as the fire damage.
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Wales have qualified for the Euro 2016 quarter finals after beating Northern Ireland 1-0 in Paris.
A rally has been held in Cardiff following the EU referendum to show support to migrant communities.
It's 0-0 at half time in Paris as Wales face Northern Ireland in the last 16 of Euro 2016.