Search of the first excited states 0+ of 108Cd and106Cd

108Cd and 106Cd nuclei have been studied from the β+/EC decay of 108In and 106In using the isocele II isotope separator working on-line with the Orsay synchrocyclotron. In order to produce indium nuclei, a molten tin target is irradiated by protons (E = 200 MeV) or 3He (E = 270 MeV). The comparison of saturation activity measured after mass separation with the one measured before mass-separation has allowed us to determine the average delay-time of indium isotopes and the overall efficiency of the separator. Single γ rays, conversion electrons rays, γ-γ-t and γ-e--t coincidence measurements have been performed to build level schemes of 108Cd and 106Cd. In 108Cd, the first excited 0+ state has been established unambiguously. This state preferably decays to the 22+ and not to the 21+ as it does in the even-even neighbouring Cd nuclei. An excited 0+ state is proposed in 106Cd. These states could not be interpreted as headstate of collective band corresponding to a shape different from the ground state one. On the other hand, the model of G. Alaga (vibrator + two proton holes), as well as the IBA2 F. Iachello one seem to be able to describe the low-lying states properties. Finally, the feeding balance and the deduced log ft values have led us to discuss the possible values of the 108In and 106In isomeric state spins