  We report 23Na NMR studies of the polycrystalline samples of bilayer hydrated
cobalt oxides Na0.35CoO2-1.3H2O with the superconducting transition
temperatures Tc < 1.8 and ~ 4.5 K. The magnitude of the 23Na nuclear
spin-lattice relaxation rate 23(1/T1) significantly decreased from non-hydrated
Na0.7CoO2 to the bilayer hydrates. We found that the temperature dependence of
23(1/T1) of the non-superconducting bilayer hydrate is similar to that of the
non-hydrated Na0.7CoO2, the spin dynamics of which is understood by A-type
(intra-layer ferromagnetic and inter-layer antiferromagnetic) spin
fluctuations. The superconducting phase is located close to the A-type magnetic
instability.
