We have examined the 12 500 Kekule valence structures of C-60 and were able to classify them in six classes, belonging to different degrees of freedom (df). There is but one Kekule structure having the maximal number of df = 10, followed by 80 Kekule valence structures with df = 9, and so on (see Table 1). In all there are only 158 essentially different Kekule valence structures out of 12 500 structures of C-60. As illustrated on Kekule structures of df = 9 there are considerable variations in the patterns of CC single and CC double bonds among different Kekule valence structures, even for structures having the same degree of freedom. (C) 2004 Published by Elsevier B.V.