Auden joked that he was the only member of his family who didn't get a divorce...
Auden met Erika through a mutual friend, Christopher Isherwood. Erika and Isherwood had been in love, and Erika had asked Isherwood to marry her so she could obtain a British passport. She had taken an open stance against fascism, and thus faced possible arrest. Isherwood said no, but told her to contact Auden. Auden agreed to marry Erika, even though the two had never met. They married, though neither of them had feelings for the other. They never lived together, and rarely saw each other. They never divorced, though, and remained legally married until Erika's death in 1969. Both Auden and Erika were actually gay, and each had different lovers.
http://www.biography.com/people/wh-auden-9192132#awesm=~oFd1l7E91c3FEe