Adsorption and desorption of N-2 molecules onto cationic Ta and Rh clusters in the gas phase were investigated in the temperature range of 300-1000 K by using thermal desorption spectrometry in combination with density functional theory (DFT) calculations. For Ta-6(+), the first N-2 molecule was found to adsorb dissociatively, and it remained adsorbed when Ta6+N2 was heated to 1000 K. In contrast, the second and the subsequent N-2 molecules adsorbed weakly as a molecular form and were released into the gas phase when heated to 600 K. The difference can be explained in terms of the activation barrier between the molecular and dissociative forms. On the other hand, when Ta clusters were generated in the presence of N-2 gas by the laser ablation of a Ta rod, isomeric clusters, TanNm+, having heat resistivity were formed. For R-h(6)+, N-2 adsorbed molecularly at 300 K and desorbed totally at 450 K. These results were consistent with the DFT calculations, indicating that the dissociative adsorption of N-2 is endothermic.