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"I eloped and ran off to Texas," Plant tells U.K. newspaper The Independent. "So now I spend half my time there and half here."
The 63-year-old rock legend went on to report that he and his fellow Grammy winner are living in an "old crack house" in Austin that's infested with termites. "I tap my hand on the table and they fly out the walls in this huge cloud, like something from a Disney film," he said.
It's unclear if Plant was serious about eloping and if so, when and where the nuptials took place. The singer and Griffin were photographed together back in November, both sporting what appeared to be wedding rings. If they are indeed husband-and-wife, this is Plant's second marriage. He divorced Maureen Wilson, the mother of his three children, in 1983. Griffin was also married once before and divorced in 1992.
Along with friend and fellow collaborator Buddy Miller, Griffin appeared on Plant's 2010 Band of Joy album and also joined the tour in support of the new music.