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We construct a nerve from double categories into double ( ∞ , 1 ) -categories and show that it gives a right Quillen and homotopically fully faithful functor between the model structure for weakly horizontally invariant double categories and the model structure on bisimplicial spaces for double ( ∞ , 1 ) -categories seen as double Segal objects in spaces complete in the horizontal direction. We then restrict the nerve along a homotopical horizontal embedding of 2 -categories into double categories, and show that it gives a right Quillen and homotopically fully faithful functor between Lack’s model structure for 2 -categories and the model structure for 2 -fold complete Segal spaces. We further show that Lack’s model structure is right-induced along this nerve from the model structure for 2 -fold complete Segal spaces.