Experimental evidence for shape coexistence in the N=59 isotone 97Sr is presented. The ground state and the lowest excited levels are confirmed to be spherical. At 585.1 keV, a K=3/2 rotational band built on the v[422 3/2] Nilsson configuration has been identified. Nilsson orbital assignments for three further levels of deformed origin are proposed. The results are compared to RPA shell-model predictions.For the 38Sr, 3gY and 4oZr nuclei near A=IO0, a sudden onset of strong deformation at N=60 has been observed, whereas the lighter isotopes up to N=58 keep a spherical shape [1]. This raises the question about the nature of the N=59 intermediate nuclei. The striking similarities between the lowest excited levels in the N=59 isotones 97Sr and 99Zr on the one hand, and the spherical N=57 isotones 95Sr and 97Zr on the other hand [2][3][4] suggest sphericity for the low-excitation region of 97Sr. Recent Laser-spectroscopic measurements have furthermore shown that ~TSr has a groundstate (g.s.) spin of I=1/2 which has been interpreted as a vsl/2 shell-model state [5]. On the other hand, quasi-particle RPA calculations [6] have shown that the overall shape of the GamowTeller (GT) strength function of ~TSr could only be reproduced when strong prolate deformation was assumed [7]. Therefore, we have carefully reinvestigated the level scheme of 97Sr in order to search for a possible rotational band as a clear signature of deformation, and with this of shape coexistence in this N=59 isotone.The isotope 97Sr was produced as ~-decay daughter of 97Rb at the on-line mass separator OSTIS [8] at the ILL Grenoble. Singles and ~-~-t coincidence spectra have been recorded. Conversion coefficients were determined by the fluorescence method. For the lifetime measurements the centroid-shift method was used [9].According to the recent spin determination [5], to the GT-decay properties of 97Sr to 97y, and to our shell-model calculations [6,7], the J==1/2 § g.s. of 97Sr is associated to the spherical (~2~ 0.05) neutron configuration (gT/2)zsl/2. This assignment, together with the known multipolarities of the ~-transitions [3], allows to deduce J~= 3/2 + , respectively 7/2 + for the first two excited states at 167 and 308 keV (see Fig. I). These levels have a character quite similar to the corresponding ones in the spherical N=57 isotopes 95 97 Sr and Zr. With this interpretation, the isomeric character (t~/2=170 ns) of the g7/2 state at 308 keV results from the E2 deexcitation to the first excited level with a transition rate close to the single-particle value, and is not associated with the ~ [404 9/2] intruder as proposed in [10]. Thus, the lowest levels of 97Sr have spherical character.In contrast, the levels at 585.1 and 687.1 keV [3] together with the new level at 822.4 keV (see Fig. 1) are proposed to form a rotational band. The first two states are populated in ~-decay of the ~[431 3/2] g.s. of 97Rb with log(ft)=5.6, each, allowing I n= (i/2-5/2) + for both of them. Selection rules for ~-transitions further limit the sp...