Full geometric optimization of endo,endo-tetracyclo[184.108.40.206(3,6).0(2,7)]dodeca-4,9-diene (TTDD) has been carried out by ab initio and DFT/B3LYP methods and the structure of the molecule investigated. The double bonds of TTDD molecule are endo pyramidalized. The structure of pi-orbitals and their mutual interactions for TTDD molecule were investigated. The cationic intermediates and products obtained as a result of the addition reaction have been studied using the HF/6-311G(d), HF/6-311G(d,p) and B3LYP/6-311G(d) methods. The bridged bromonium cation isomerized into the more stable N- and U-type cations and the difference between the stability of these cations is small. The N- and U-type reaction products are obtained as a result of the reaction, which takes place via the cations in question. The stability of exo, exo and exo, endo isomers of N-type product are nearly the same and the formation of both isomers is feasible. The U-type product basically formed from the exo, exo-isomer. Although the U-type cation was 0.68 kcal mol(-1) more stable than the N-type cation, the U-type product was 4.79 kcal mol(-1) less stable than the N-type product.