[en] In this paper it is shown that the density functional theory can be generalized to systems with degenerate excited states. There is a one-to-one map between the subspace, spanned by the ground state and any one of the first degenerate excited states, and the sum of their densities. But only a one way correspondence exists between external potential and subspace, as well as between external potential and the sum of densities. The extension of the Hohenberg-Kohn-Sham theory for degenerate excited states has also been developed. (author)