Recent interest in spectroscopic factors for single-neutron transfer in low-spin states of the even–odd Xenon 125,127,129.131Xe and even–odd Tellurium, 123,125,127,129,131Te isotopes stimulated us to study these isotopes within the framework of the Interacting Boson–Fermion Model. The fermion that is coupled to the system of bosons is taken to be in the positive parity 3s1/2, 2d3/2, 2d5/2, 1g7/2 and in the negative 1h11/2 single-particle orbits, the complete 50–82 major shell. The calculated energies of low-spin energy levels of the odd isotopes are found to agree well with the experimental data. Also, B(E2), B(M1) values and spectroscopic factors for single-neutron transfer are calculated and compared with experimental data.