The hyperbranched polyester based on 4,4-bis-(4-hydroxyphenyl)pentanoic acid was synthesized with different DP's. A complete H-1 and C-13 NMR assignment of the oligomers was carried out. Six different structural units were quantified by NMR analysis. The conversion dependence of the content of these structural units and of the degree of branching DB follows the theoretically derived equations. Furthermore, six different diads were quantified by C-13 NMR spectroscopy. The conversion dependence of the diads was calculated and again the measured data agree well with the theory. The good fit between theoretical and measured data proves, that the polycondensation of the 4,4-bis-(4'-hydroxyphenyl)pentanoic acid follows a random growth of the different units with equal reaction rates of all reaction steps. Finally, spin-lattice relaxation times (T-1C) and nuclear Overhauser enhancements (NOE) were determined and discussed.