The current paradigm of eukaryotic evolution is based primarily on comparative analysis of ribosomal RNA sequences. It shows several early–emerging lineages, mostly amitochondriate, which might be living relics of a progressive assembly of the eukaryotic cell. However, the analysis of slow–evolving positions, carried out with the newly developed slow–fast method, reveals that these lineages are, in terms of nucleotide substitution, fast–evolving ones, misplaced at the base of the tree by a long branch attraction artefact. Since the fast–evolving groups are not always the same, depending on which macromolecule is used as a marker, this explains most of the observed incongruent phylogenies. The current paradigm of eukaryotic evolution thus has to be seriously re–examined as the eukaryotic phylogeny is presently best summarized by a multifurcation. This is consistent with the Big Bang hypothesis that all extant eukaryotic lineages are the result of multiple cladogeneses within a relatively brief period, although insufficiency of data is also a possible explanation for the lack of resolution. For further resolution, rare evolutionary events such as shared insertions and/or deletions or gene fusions might be helpful.