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We present our NMR studies of double-layer hydrated cobalt oxidesNaxCoO2-yH2O (x ~ 0.35, y ~ 1.3) with various Tc = 0 - 4.8 K and magnetictransition temperatures. High-resolution $^{1}$H NMR spectrum served as anevidence for the existence of H$_{3}$O$^{+}$ oxonium ions. $^{23}$Na nuclearspin-lattice relaxation rates served to detect local field fluctuationssensitive to Tc. $^{59}$Co nuclear quadrupole resonance (NQR) spectra served toclassify the various Tc samples. From the classification by $^{59}$Co NQRfrequency, the double-layer hydrated compounds were found to have twosuperconducting phases closely located to a magnetic phase. In the normal stateand at a magnetic field in the $ab$-plane, two $^{59}$Co NMR signals withdifferent Knight shifts and different $^{59}$Co nuclear spin-lattice relaxationtimes $^{59}T_{1}$ were observed. The two $^{59}$Co NMR signals suggestmagnetic disproportionation of two Co sites or in-plane (XY) anisotropy of asingle Co site. Non Korringa behavior and power law behavior in zero-field NQR1/$^{59}T_{1}$ above and below Tc suggest non-Fermi liquid and unconventionalsuperconductivity.

59Co, 23Na, and 1H NMR Studies of Double-Layer Hydrated Superconductors NaxCoO2-yH2O