  We prove that a sum of free non-covariant duality-symmetric actions does not
allow consistent, continuous and local self-interactions that deform the gauge
transformations. For instance, non-Abelian deformations are not allowed, even
in 4 dimensions where Yang-Mills type interactions of 1-forms are allowed in
the non-manifestly duality-symmetric formulation. This suggests that
non-Abelian duality should require to leave the standard formalism of
perturbative local field theories. The analyticity of self-interactions for a
single duality-symmetric gauge field in four dimensions is also analyzed.
