A study of the Ga2Te3 and Ga3Te2 clusters is presented using three different levels of theory, namely; DFT, MP2 and CCSD(T). We used the 6-311G(d) basis set for gallium atom and the LANL2DZdp ECP basis set for tellurium atom. The results include geometrical parameters, vibrational frequencies and energies of the low-lying structures. We report the vertical electron detachment energy (VEDE) and adiabatic electron detachment energy (AEDE) for the anionic species. The neutral Ga2Te3 cluster adopts a V-shape configuration with (1)A(1) ground state whilst its anion is kite shaped with (2)A(1) ground state. On the other hand, the Ga3Te2 and Ga3Te2- species prefer a three dimensional 6-D-3h geometry with (2)A(2)'' and (1)A(1)' electronic states, respectively. The adiabatic electron affinity (AEA) for Ga2Te3 is 2.78 eV and that of Ga3Te2 is 2.86 eV at the CCSD(T)//B3LYP level. We analyse, discuss and compare the findings of our research with the analogous gallium chalcogenides.