Fast-timing measurements were performed on ^137,139Cs obtained from the β^- decay of ^137,139Xe. The neutron-rich Xe nuclei were produced by the ²³⁸IJ photofission induced by the 50 MeV electron beam delivered by the ALTO facility. The half-lives of the first excited state in ¹³⁷Cs and of six excited states in ¹³⁹Cs were measured for the first time. These T_1/2 results give new information on the structure of the ^137,139₅₅Cs_82,84 nuclei located near the neutron closed shell N = 82. In particular, 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. From the comparison with other N = 84 isotones, the most probable spin values for the states located at 289.8, 393.5, and 393.8 keV in ¹³⁹Cs appear to be 5/2⁺, 3/2⁺, and 1/2⁺.