The prokaryotic tubulin homolog FtsZ polymerizes into a ring structure essential for bacterial cell division. We have used refolded FtsZ to crystallize a tubulin-like protofilament. The N- and C-terminal domains of two consecutive subunits in the filament assemble to form the GTPase site, with the C-terminal domain providing water-polarizing residues. A domain-swapped structure of FtsZ and biochemical data on purified N- and C-terminal domains show that they are independent. This leads to a model of how FtsZ and tubulin polymerization evolved by fusing two domains. In polymerized tubulin, the nucleotide-binding pocket is occluded, which leads to nucleotide exchange being the rate-limiting step and to dynamic instability. In our FtsZ filament structure the nucleotide is exchangeable, explaining why, in this filament, nucleotide hydrolysis is the rate-limiting step during FtsZ polymerization. Furthermore, crystal structures of FtsZ in different nucleotide states reveal notably few differences.