Dating the age of the universe by the β-decay of 187Re (t1/2 = 41.2 Gyr) requires the accurate assessment of the s-process reaction flow. The daughter nucleus 187Os as well as its immediate s-only neighbor 186Os are shielded from the r-process. Therefore, the radiogenic contribution to 187Os can be derived via the local approximation of the s-process, which is well justified in this mass region: ( σ Ns)187 = ( σ Ns)186. Accordingly, accurate Maxwellianaveraged (n, γ ) cross sections have to be known for 186Os and 187Os over the full range of s-process temperatures. Because 187Os has low-lying excited states, which are significantly populated during the s-process, neutron captures on these excited states have to be properly taken into account. The input for the corresponding Hauser–Feshbach calculations can be constrained by deriving the strength functions from a detailed resonance analysis of the measured (n, γ ) cross sections as well as by an additional measurement of the inelastic scattering cross section for the first exited level, which dominates the competition between the capture and scattering channels. This contribution reports on measurements of the neutron capture cross sections of 186Os, 187Os and 188Os from the eV region to 1MeV at the CERN/n TOF facility and of the inelastic scattering cross section of 187Os around 30 keV at the Karlsruhe 3.7 MV Van de Graaff accelerator. Based on these results and on a detailed resonance analysis, improved Maxwellian-averaged cross sections were obtained for thermal energies between 5 keV and 100 keV. The implications of these results for the Re/Os clock are discussed.