On the assumption that the double-coiled pattern of microtubules in the axoneme of Echinosphaerium might be due to links of two sizes between adjacent microtubules, we disassembled microtubules with low temperature and then carefully analyzed the patterns of microtubules that formed upon the addition of heat (22 degrees C) or heat and D(2)O. Although most of the initial clusters of microtubules that formed could not be interpreted as part of an axoneme, the spacings between these microtubules were the same as that in the axoneme, 70 and 300 A. By model building we were able to show that all clusters that form, including stages in the formation of the axoneme and its 12-fold symmetry, could be explained by links of two sizes (70 and 300 A) and the substructure of the microtubule. We could demonstrate these links with improved staining methods. We suggest that nonaxonemal assemblies of microtubules may be eliminated by the natural selection of the most energetically stable configuration of microtubules, all others undergoing disassembly under equilibrium conditions. Model building further supports this suggestion since the model axoneme possesses more links per tubule than any other cluster found.