Magnetic dipole and electric quadrupole moments of nuclei in the light-mass neutron-rich region have been studied by taking advantage of spin-polarized radioactive nuclear beams that have been obtained from the projectile fragmentation reaction. Analyses of the results reveal a few interesting phenomena characteristic of nuclear structures in this region. In particular, we report in some detail the latest result on the magnetic moment of the 17 C ground state. The distinctly small value of the g-factor obtained, | g(C-17 | = 0.5054 +/- 0.0025, clearly excludes a I-pi = 1/2(+) candidate for the spin-parity assignment of this marginally bound nucleus, providing a reasonable account of the non-halo nature reported in recent breakup reaction experiments. Finally, future plans at the upcoming radioactive beam facility presently under construction at RIKEN are briefly mentioned.