Spermatozoa of the gall midge, Asphondylia ruebsaamen, were found to have an axoneme with about 2500 microtubular doublets, each carrying a single dynein arm that corresponds to the outer dynein arm of conventional flagella. The doublets form a tightly wound double spiral, in which doublets of the inner spiral and outer one are joined pairwise. Whereas most axonemes had their doublets in a curved spiral, some axonemes showed large blocks of doublets lying in a rather regular crystalline arrangement. The axoneme hence could appear in two states, spiral and crystalline, with intermediate forms. The doublets and their dynein arms and other connections have been subjected to a computer analysis that aims at calculating an average image from a great number of doublet pairs. Two strategies of image analysis were used. In one method the average doublet pair was obtained from a number of isolated image motifs by correlation methods; this strategy could be applied to both the spiral regions and crystalline ones and showed that there are definite differences in the angle between the two doublets of a pair and in the greater regularity of the dynein arm orientation in the crystalline state. Further, it can be seen that the shape of the two doublets in the pair is the same in the spiral regions and differs somewhat in the crystalline one. In the other strategy a filtration of noisy components was performed from the Fourier transform of periodic arrays portrayed in crystalline regions. This strategy included a determination of distortions in the lattice, and removal of these distortions by image resampling in iterated steps. The average doublet pairs appear much the same in reconstructions made with either strategy. It could be seen that the interspace between the microtubular protofilaments varied somewhat and appeared widened at those places where the dynein arm or other bridges were inserted. The lumen of the microtubules could also be seen to have slender radial strands that are particularly well resolved in the B-tubules of the doublets in the spiral state. The axoneme was seen to have one polypeptide band only in the dynein band region.