General guidelines for the design of monomers for the synthesis of hyperbranched polymers without linear units are presented. The synthesis of one monomer fulfilling these requirements and the first results of the polymerization of this monomer are described. 4-(3-Maleimidopropoxy)-4'-methoxybenzaldehyde azine was used as a monomer of the AB(2)-type in a "criss-cross" cycloaddition with the maleimide group as A-function and the azine as two B-groups. Melt condensation of this monomer gave a polymer ((M) over bar(n) = 5700) which showed H-1 and C-13 NMR spectra corresponding well to the expected completely branched structure.