We report intensive studies on the cobalt oxide superconductors NaxCoO2·1.3H2O via 59 Co NMR and NQR measurements. In the sample with x=0.26 and Tc=4.6, we find that the spin–lattice relaxation rate 1/T1 shows a T3 variation below Tc 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 Tc via the Knight shift measurement. The spin part of the Knight shift decreases below Tc 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.