Vibration frequencies of the NCO stretching mode were calculated for model molecules of the copper ion-exchanged ZSM-5 catalytic system, Cu(OH 2 ) 3 X n + (X = NCO, NCO - and HNCO, n = 1 or 2) by use of ab initio molecular orbital calculations. The complexes, Al(OH) 3 (NCO), Al(OH) 3 (NCO - ) and Al(OH) 3 (OCNH) were adopted as the models of the zeolite framework. According to the present calculations, the absorption bands observed at 2189 cm - 1 and 2251 cm - 1 are assigned to the stretching vibration of the NCO - coordinating to the copper ion and to the aluminum in the zeolite (ZSM-5) framework, respectively. This result is consistent with the experimental assignment.