The neutron capture cross section of some unstable nuclei is especially relevant for s-process nucleosynthesis studies. This magnitude is crucial to determine the local abundance pattern, which can yield valuable information of the s-process stellar environment. In this work we describe the neutron capture (n,¿) measurement on two of these nuclei of interest, 204Tl and 171Tm, from target production to the final measurement, performed successfully at the n_TOF facility at CERN in 2014 and 2015. Preliminary results on the ongoing experimental data analysis will also be shown. These results include the first ever experimental observation of capture resonances for these two nuclei.