  It is shown that the modulus of any graded or, more generally, twisted KMS
functional of a C*-dynamical system is proportional to an ordinary KMS state
and the twist is weakly inner in the corresponding GNS-representation. If the
functional is invariant under the adjoint action of some asymptotically abelian
family of automorphisms, then the twist is trivial. As a consequence, such
functionals do not exist for supersymmetric C*-dynamical systems. This is in
contrast with the situation in compact spaces where super KMS functionals occur
as super-Gibbs functionals.
