The cyclic three-membered bromonium and iodonium ions of adamantylideneadamantane (Ad=Ad; 1) have been prepared and characterized as their triflate salts (I-Br+/OTf-; 1-1+/OTf-) by X-ray diffraction. The X-ray diffraction data indicate that the halonium ion portions of 1-Br+/OTf- and 1-1+/OTf- are essentially symmetrical with the following averaged structural parameters : Br-C, 2.11 angstrom; C-C, 1.49 angstrom; Br-C-C angle, 69.4-degrees; C-Br-C angle, 41.3-degrees; I-C, 2.48 angstrom; C-C, 1.45 angstrom; I-C-C angle, 72-degrees; C-I-C angle, 36-degrees. The C-13 NMR spectra of these ions and the bromonium and iodonium ions of bicyclo[3.3.1]nonylidenebicyclo[3.3.l]nonane (2) have been investigated in CH2Cl2. At low temperatures, the C-13 NMR spectra of 1-X+ (X = Br, I) and 2-1+ indicate that the halonium ion has two perpendicular planes of symmetry. Addition of the parent olefin causes line broadening of certain signals attributable to the carbon atoms above and below a plane that includes the central C-C bond and is perpendicular to the above two planes. The broadening suggests that small amounts of parent olefin can translocate the X+ from the top side of a given halonium ion to its bottom side. Line-shape analysis yields the pseudo-first-order rate constant for site exchange at each concentration of added parent olefin. For 1-Br+, 1-I+, and 2-I+, the respective second-order rate constants for this site exchange are 2.0, 7.6, and 4.2 X 10(6) M-1 s-1 at -80-degrees-C. The activation parameters for the site exchange between I-Br+ and Ad=Ad are DELTAH(double dagger) = 1.8 kcal/mol and DELTAS(double dagger) = -21 eu. High-level ab initio calculations on the model system C2H4X+ + C2H4 half arrow right over half arrow left C2H4 + C2H4X+ indicate that the transfer proceeds via an unsymmetrical 1:1 halonium ion/olefin charge-transfer complex intermediate and a symmetrical D2d transition state.