Prokaryotes constitute a single kingdom, Bacteria, here divided into two new subkingdoms: Negibacteria, with a cell envelope of two distinct genetic membranes, and Unibacteria, comprising the new phyla Archaebacteria and Posibacteria, with only one. Other new bacterial taxa are established in a revised higher-level classification that recognizes only eight phyla and 29 classes. Morphological, palaeontological and molecular data are integrated into a unified picture of large-scale bacterial cell evolution despite occasional lateral gene transfers. Archaebacteria and eukaryotes comprise the clade neomura, with many common characters, notably obligately co-translational secretion of N-linked glycoproteins, signal recognition particle with 7S RNA and translation-arrest domain, protein-spliced tRNA introns, eight-subunit chaperonin, prefoldin, core histones, small nucleolar ribonucleoproteins (snoRNPs), exosomes and similar replication, repair, transcription and translation machinery. Eubacteria (posibacteria and negibacteria) are paraphyletic, neomura having arisen from Posibacteria within the new subphylum Actinobacteria (possibly from the new class Arabobacteria, from which eukaryotic cholesterol biosynthesis probably came). Replacement of eubacterial peptidoglycan by glycoproteins and adaptation to thermophily are the keys to neomuran origins. All 19 common neomuran character suites probably arose essentially simultaneously during the radical modification of an actinobacterium. At least 11 were arguably adaptations to thermophily. Most unique archaebacterial characters (prenyl ether lipids; flagellar shaft of glycoprotein, not flagellin; DNA-binding protein lob; specially modified tRNA; absence of Hsp90) were subsequent secondary adaptations to hyperthermophily and/or hyperacidity. The insertional origin of protein-spliced tRNA introns and an insertion in proton-pumping ATPase also support the origin of neomura from eubacteria. Molecular co-evolution between histones and DNA-handling proteins, and in novel protein initiation and secretion machineries, caused quantum evolutionary shifts in their properties in stem neomura. Proteasomes probably arose in the immediate common ancestor of neomura and Actinobacteria. Major gene losses (e.g. peptidoglycan synthesis, hsp90, secA) and genomic reduction were central to the origin of archaebacteria. Ancestral archaebacteria were probably heterotrophic, anaerobic, sulphur-dependent hyperthermoacidophiles; methanogenesis and halophily are secondarily derived. Multiple lateral gene transfers from eubacteria helped secondary archaebacterial adaptations to mesophily and genome re-expansion. The origin from a drastically altered actinobacterium of neomura, and the immediately subsequent simultaneous origins of archaebacteria and eukaryotes, are the most extreme and important cases of quantum evolution since cells began. All three strikingly exemplify De Beer's principle of mosaic evolution: the fact that, during major evolutionary transformations, some organismal characters are highly innovative and change remarkably swiftly, whereas others are largely static, remaining conservatively ancestral in nature. This phenotypic mosaicism creates character distributions among taxa that are puzzling to those mistakenly expecting uniform evolutionary rates among characters and lineages. The mixture of novel (neomuran or archaebacterial) and ancestral eubacteria-like characters in archaebacteria primarily reflects such vertical mosaic evolution, not chimaeric evolution by lateral gene transfer. No symbiogenesis occurred. Quantum evolution of the basic neomuran characters, and between sister paralogues in gene duplication trees, makes many sequence trees exaggerate greatly the apparent age of archaebacteria. Fossil evidence is compelling for the extreme antiquity of eubacteria [over 3500 million years (My)] but, like their eukaryote sisters, archaebacteria probably arose only 850 My ago. Negibacteria are the most ancient, radiating rapidly into six phyla. Evidence from molecular sequences, ultrastructure, evolution of photosynthesis, envelope structure and chemistry and motility mechanisms fits the view that the cenancestral cell was a photosynthetic negibacterium, specifically an anaerobic green non-sulphur bacterium, and that the universal tree is rooted at the divergence between sulphur and non-sulphur green bacteria. The negibacterial outer membrane was lost once only in the history of life, when Posibacteria arose about 2800 My ago after their ancestors diverged from Cyanobacteria.