Prokaryotic cell division protein FtsZ, an assembling GTPase, directs the formation of the septosome between daughter cells. FtsZ is an attractive target for the development of new antibiotics. Assembly dynamics of FtsZ is regulated by the binding, hydrolysis and exchange of GTP. We have determined the energetics of nucleotide binding to model apo-FtsZ from Methanococcus jannaschii and studied the kinetics of mant-nucleotide binding and dissociation from FtsZ polymers, employing calorimetric, fluorescence and stopped-flow methods. FtsZ binds GTP and GDP with Kb values ranging from 20 to 300 M^-1 under various conditions. GTP•Mg² and GDP•Mg²⁺ bind with slightly reduced affinity. Bound GTP and the coordinated Mg²⁺ ion play a minor structural role in FtsZ monomers, but Mg²⁺-assisted GTP hydrolysis triggers polymer disassembly. Mant-GTP binds and dissociates quickly from FtsZ monomers, with ~10-fold lower affinity than GTP. Mant-GTP displacement measured by fluorescence anisotropy provides a method to test the binding of any competing molecules to the FtsZ nucleotide site. Mant-GTP is very slowly hydrolyzed and remains exchangeable in FtsZ polymers, but the complex becomes kinetically stabilized, with a 30-fold slower k₊ and ~500-fold slower k_- than in monomers. Mant-GTP dissociation rate from FtsZ polymers is comparable to GTP hydrolysis turnover and to the reported subunit turnover in Escherichia coli FtsZ polymers. Although FtsZ polymers can exchange nucleotide, unlike its eukaryotic structural homologue tubulin, GDP dissociation may be slow enough for polymer disassembly to take place first, resulting in FtsZ polymers cycling with GTP hydrolysis similarly to microtubules.