The new phases (Ba0.5Sr0.5)(7)Co6O18, Ba8Co7O21, and Ba9Co8O12 have been shown by electron diffraction and high-resolution electron microscopy to be three new members (n = 5, n = 6, and n = 7) of the 2H hexagonal perovskite-related A(n+2)B'BnO3n+3 homologous series. Their modulated structures are made up of chains, running along the c direction and separated by Ba(Sr) ions, containing a succession of one Co atom in prismatic trigonal sites and it Co atoms in octahedral coordination sharing faces. The strategy to synthesize different terms of this family is discussed in terms of the distance between AO(3) layers, (C) 1999 Academic Press.