-Monte Carlo methods were used to examine the sampling distribution of eight consensus indices based on either of the following two models: all bifurcating trees are equally likely; or all trees (including both bifurcating and multifurcating trees) are equally likely. Ten different consensus-tree methods were applied before computing consensus indices. The strictness of a consensus-tree method and the recognition ratio of a consensus index are the two main factors determining the consensus-index distribution. The former factor influences the mean index values; the latter changes the shape of the distribution curves. We furnish significance test tables for consensus trees or indices based on randomly generated trees permitting multifurcations. These tables can be used to test whether a given consensus tree or consensus-index value obtained from data on real organisms differs significantly from what one would expect if one were computing such quantities from randomly sampled trees. [Consensus indices; significance table; numerical taxonomy.] Consensus methods, including those used for the construction of consensus trees (CTs) and for the computation of consensus indices (CIs), are currently subjects of active research in numerical taxonomy. Consensus-tree methods aim at a tree that represents the joint information or consensus of two trees; consensus-index methods furnish a numerical measure of the agreement between two trees. There have been several common biological applications of consensus methods in recent numerical taxonomic studies: (1) They have been used as tests of evolutionary theory through comparisons of estimated phylogenetic trees based on different data sets (Penny et al., 1982; Rohlf et al., 1983). (2) Also, comparisons have been made of phenograms or cladograms obtained by different techniques (Sokal, 1983a). (3) Comparisons have been employed to evaluate the relative stability of phenetic and cladistic methods (Mickevich, 1978; Colless, 1980; Rohlf and Sokal, 1980; Schuh and Farris, 1981; Sokal and Rohlf, 1981; Sokal, 1983b; Sokal et al., 1984). Such studies investigate stability when based on random samples or bipartitions of characters or OTUs (Schuh and *1 Present address: Institute of Zoology, Academia Sinica, Nankang, Taipei, Taiwan, Republic of China. Farris, 1981; Sokal and Shao, 1985). The problem investigated is termed congruence when different classes of characters of the same organism are used in the comparison (Mickevich, 1978; Rohlf and Sokal, 1980; Mickevich and Farris, 1981; Rohlf et al., 1983a, b). (4) Finally, they have been used to test the accuracy of cladogram estimation in those few cases where true trees are known (Sokal, 1983a; Fiala and Sokal, 1985). The statistical significance of consensus indices produced in such tests is an obvious concern. For instance, is a CI value produced by a given method and based on data from real organisms significantly different from one produced by the same method for randomly sampled trees? Only one paper investigating CI distributions has been published. Shao and Rohlf (1983) have furnished significance-test tables for seven consensus indices based on strict and Adams-2 consensus trees between strictly bifurcating trees. In this study, we report on and provide significance-test tables for most currently available CT and CI meth-