  Non-quasiparticle (incoherent) states which play an important role in the
electronic structure of half-metallic ferromagnets (HMF) are investigated
consistently in the case of antiferromagnetic $s-d(f)$ exchange interaction.
Their appropriate description in the limit of strong correlations requires a
rearrangement of perturbation series in comparison with the usual Dyson
equation. This consideration provides a solution of the Kondo problem in the
HMF case and can be important for first-principle HMF calculations performed
earlier for ferromagnetic $s-d(f)$ interaction.
