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 relies 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.