A fast-timing setup has been developed to measure the nuclear-state half-lives of neutron-rich nuclei. The first on-line measurements were performed on 137,139 Cs obtained from the β − decay of 137,139 Xe. These neutron-rich Xe nuclei were produced by the 238 U photofission induced by the 50 MeV electron beam delivered by the ALTO facility. The half-lives of the first excited state in 137 Cs and of six excited states in 139 Cs were measured for the first time. Taking into account new information given by the deduced transition probabilities, we discuss the structure of the first excited states in 137,139 Cs: it is shown that, in both nuclei, the first excited 5 2 + level corresponds mainly to the one-proton state issued from the π2d 5/2 orbital and that the most probable spin values for the states located at 289.8, 393.5, and 393.8 keV in 139 Cs are 5 2