How many primary lineages of life exist and what are their evolutionary relationships? These are fundamental but highly controversial issues. Woese and co-workers propose that archaebacteria, eubacteria and eukaryotes are the three primary lines of descent and their relationships can be represented by Fig. 1a (the 'archaebacterial tree') if one neglects the root of the tree. In contrast, Lake claims that archaebacteria are paraphyletic, and he groups eocytes (extremely thermophilic, sulphur-dependent bacteria) with eukaryotes, and halobacteria with eubacteria (the 'eocyte tree', Fig. 1b). Lake's view has gained considerable support as a result of an analysis of small subunit ribosomal RNA sequence data by a new approach, the evolutionary parsimony method. Here we report that analysis of small subunit data by the neighbour-joining and maximum parasimony methods favours the archaebacterial tree and that computer simulations using either the archaebacterial or the eocyte tree as a model tree show that the probability of recovering the model tree is very high (greater than 90 per cent) for both the neighbour-joining and maximum parsimony methods but is relatively low for the evolutionary parsimony method. Moreover, analysis of large subunit rRNA sequences by all three methods strongly favours the archaebacterial tree.