We report intensive studies on the cobalt oxide superconductors NaxCoO2 center dot 1.3H(2)O via Co-59 NMR and NQR measurements. In the sample with x = 0.26 and T-c = 4.6, we find that the spin-lattice relaxation rate 1/T-1 shows a T-3 variation below T-c and down to very low temperatures, which indicates the presence of line nodes in the superconducting (SC) gap function. We have also studied the spin susceptibility below T-c via the Knight shift measurement. The spin part of the Knight shift decreases below T-c in both the a- and c-directions indicating singlet spin state of the Cooper pairs. Our results strongly suggest that the superconducting state is a d-wave state. (c) 2006 Elsevier B. V. All rights reserved.