"Physics with spin-oriented exotic nuclear beams and examples of measurements of nuclear moments" Dimiter Balabanski An overview of a series of recent experiments aimed at the determination of the moments of exotic nuclei produced in fragmentation reactions will be given. The spin-orientation: spin-alignment or spin-polarization of the nuclear ensemble, which is produced in a fragmentation reaction, is of utmost importance for these studies. The discussion will emphasize on the open problems related to the production and the preservation of the orientation during the experiments. Pros and contras for experiments at both, intermediate energies (~ 100 MeV/A) and high energies (~ 1 GeV/A) of the exotic beams will be considered. Examples will be provided from a series of nuclear moment measurements, which were performed using the LISE3 spectrometer at GANIL. The spin-alignment and the spin-polarization of the nuclear ensemble were studied by the b-LMR and the b-NMR experimental techniques [1,2]. A devoted experiment was carried out to study systematically the orientation of Boron fragments as a function of the number of abraded nucleons in order to study the mechanism of creation of spin-orientation in fragmentation reactions. The experimental results will be discussed in the framework of the kinematical model of the fragmentation reaction [3,4]. [1] N. Coulier et al., Phys. Rev. C 59, 1935 (1999) and references therein. [2] N. Coulier et al., Phys. Rev. C 63, 054605 (2001) [3] K. Asahi et al., Phys. Lett. 251B, 488 (1992) [4] H. Okuno et al., Phys. Lett 335B, 29 (1994)