The evolutionary relationships within prokaryotes and between prokaryotes and eukaryotes is examined based on protein sequence data. Phylogenies and common signature sequences in some of the most conserved proteins point to a close evolutionary relationship between Archaebacteria and Gram-positive bacteria. The monophyletic nature and distinctness of the Archaebacterial domain is not supported by many of the phylogenies. Within Gram-negative bacteria, cyanobacteria are indicated as the deepest branching lineage, and a clade consisting of Archaebacteria, Gram-positive bacteria and cyanobacteria is supported by signature sequences in many proteins. However, the division within the prokaryotic species, viz. Archaebacteria<-->Gram-positive bacteria-->Cyanobacteria-->other groups of Gram-negative bacteria, is indicated to be not very rigid but, instead is an evolutionary continuum. It is expected that certain species will be found which represent intermediates in the above transitions. By contrast to the evolutionary relationships within prokaryotes, the eukaryotic species, which are structurally very different, appear to have originated by a very different mechanism. Protein phylogenies and signature sequences provide evidence that the eukaryotic nuclear genome is a chimera which has received major contributions from both an Archaebacterium and a Gram-negative bacterium. To explain these observations, it is suggested that the ancestral eukaryotic cell arose by a symbiotic fusion event between the above parents and that this fusion event led to the origin of both nucleus and endoplasmic reticulum. The monophyletic nature of all extant eukaryotic species further suggests that a 'successful primary fusion' between the prokaryotic species that gave rise to the ancestral eukaryotic cell took place only once in the history of this planet.