The structure of bis(cyclooctatetraenyl)zirconium, Zr(C8H8)2, has been investigated by variable-temperature solution and solid-state NMR spectroscopy and by X-ray crystallography. The solution H-1 and C-13 NMR data show that all 16 protons and all 16 carbon atoms are equivalent on the NMR time scale even at -100-degrees-C. No line broadening due to decoalescence of a fluxional process was noted, and the spectra are thus consistent with the original proposal that Zr(C8H8)2 adopts a symmetric sandwich structure. However, the CPMAS C-13 NMR spectrum contains two resonances and the X-ray crystallographic results unambiguously reveal a structure with one eta-8- and one eta-4-C8H8 ring. The exchange barrier for the fluxional process that makes the two C8H8 rings equivalent has been estimated to be < 7.5 kcal mol-1 in solution and > 13.5 kcal mol-1 in the solid state. A second fluxional process which involves 1,2-shifts of the eta-4-C8H8 ring has a much lower barrier that has been estimated to be < 5.5 kcal mol-1 in the solid state. Neither electronic nor steric factors clearly favor the asymmetric structure over the symmetric sandwich alternative. Similar conclusions are drawn for the structure of the hafnium analogue Hf(C8H8)2. Crystal data for Zr(C8H8)2 at -75-degrees-C: monoclinic; space group Pn; a = 7.049 (5), b = 7.695 (4), c = 11.217 (10) angstrom; beta = 95.08 (7)-degrees; V = 606 (1) angstrom 3; Z = 2; R(F) = 0.054; R(wF) = 0.057 for 153 variables and 1023 independent reflections with I > 2.58-sigma-(I).