The /~-decay of 377ms 95Rb and 168ms 97Rb has been thoroughly investigated by means of 7-ray, conversion electron and /Ldelayed neutron spectroscopy. More than 97 % of the /~-decay to particle-bound states has been placed in level schemes of 95Sr and 97Sr. High-resolution neutron spectroscopic studies have allowed to extend the knowledge of the excitation spectra up to 9 MeV, respectively 10 MeV. The density of neutron-unbound levels in 95Sr and 97Sr has been derived from peak stripping analyses of the neutron spectra. Beta-strength functions (S~(E)) have been investigated in detail.They indicate that Gamow-Teller /~-decay of both precursors is dominated by nuclear structure. The discovered pronounced resonances and the variation in the shape of So(E ) are compared with predictions from the gross theory of/3-decay and shell model calculations in the random phase approximation (RPA).