We present our NMR studies of double-layer hydrated cobalt oxides NaxCoO2-yH2O (x ~ 0.35, y ~ 1.3) with various Tc = 0 - 4.8 K and magnetic transition temperatures. High-resolution H NMR spectrum served as an evidence for the existence of HO oxonium ions. Na nuclear spin-lattice relaxation rates served to detect local field fluctuations sensitive to Tc. Co nuclear quadrupole resonance (NQR) spectra served to classify the various Tc samples. From the classification by Co NQR frequency, the double-layer hydrated compounds were found to have two superconducting phases closely located to a magnetic phase. In the normal state and at a magnetic field in the -plane, two Co NMR signals with different Knight shifts and different Co nuclear spin-lattice relaxation times were observed. The two Co NMR signals suggest magnetic disproportionation of two Co sites or in-plane (XY) anisotropy of a single Co site. Non Korringa behavior and power law behavior in zero-field NQR 1/ above and below Tc suggest non-Fermi liquid and unconventional superconductivity.

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