The fractal behavior of soot agglomerates formed by the combustion of acetylene in a coannular diffusion burner is studied. Structural data from electron micrographs were obtained by two methods: the first by particle counting with the aid of stereopairs for small clusters, and the second by electronic digitization with advanced image processing techniques, used for the larger agglomerates. An average agglomerate length to width ratio of about 1.7 with a standard deviation of 0.6 was obtained. The agglomerates were found to have a fractal dimension of about 1.8-1.9 based on measurements of the pair correlation function for large agglomerates and 1.5-1.6 based on measurements of the radius of gyration for small agglomerates. These results are compared with recent computer simulations as well as experimental studies of inorganic smokes.