Transketalization reactions between the diketals of 1,4-cyclohexanedione and the diketonides of pentaerythritol yield a spiropolymer which is insoluble in all solvents tried, but which can be hydrolysed to 1,4-cyclohexanedione and pentaerythritol. At short reaction times, oligomers such as 3,3,21,21-tetramethyl-1,5,10,14,19,23,26,29-octaoxapentaspiro[5.2.2.2.2.5.2.2.2.2.2]untriacontane can be isolated. However, all attempts to achieve a genuine equilibrium between the monomers, oligomers and polymer were fruitless. The C-13 cross-polarization/magic angle spinning (CP/MAS) n.m.r. spectrum of the polymer shows extra lines relative to those of soluble model compounds; this is probably due to a slow ring inversion of the 1,3-dioxane rings in the solid polymer.