Patterns of correlation of asymmetry values among characters among individuals and populations are equivocal. In general, no significant correlation between characters is found among individuals, yet there are often significant correlations among populations. That is, if an individual is more symmetrical than another for one character, there is no tendency for it to be more symmetrical for any other character, yet if a given population is more symmetrical than another for one character, there is a tendency for it also to be more symmetrical for other characters. However, previous results have been heterogeneous. Here, existing data sets from 50 samples representing 11 invertebrate species are examined for correlation patterns within individuals and populations. Using Kendall's coefficient of concordance, it was found that, although there are significant consistent differences in the level of asymmetry among different characters within individuals and populations, there was no evidence of significant concordance among individuals or populations. The results indicate that the genetic basis of developmental stability is character, population and taxon specific.