The thermal-neutron capture cross sections for the reactions 128Te (n,γ) 129gTe and 128Te (n,γ) 129mTe have been measured by a neutron activation method, using gold as a standard. Samples of powdered tellurium enriched to 96.5% in 128Te were measured by gamma spectrometry. The found values are 199.7 ± 8 and 16.1 ± 0.7 mb, respectively. The resonance integrals have been calculated by irradiating tellurium and gold, or cobalt, with and without cadmium covers; their values are 1.48 ± 0.13 b and 77.4 ± 5.2 mb, respectively.