Let Kn(D) be a class of analytic in domain D functions such that [F(z); z0,...,zn] for any z0,...,zn ∈ D. The domain D is called by maximal Kn-domain of the family T of functions which are analytic in D, if for any neighborhood ε(ψ) of any boundary point ψ of D there exists a function from T which does not belong to Kn(D \smile ε(ψ)). The maximal domain of univalence, i.e., maximal K1 domain was investigated by Bulgarian mathematician L. Chakalov. In this paper as maximal Kn-domains the angular domains are examined. Kn-domains for two special classes of rational functions are established.