Abstract We have carried out Ru NMR and NQR measurements in superconductor CeRu2 having Tc = 6.1 K in the temperature range of 1.3-30 K. From the 99Ru NMR in 10.2 T above Hc2 , T1T = const was found in the measured-T range, and the value of T1TK2 is almost the same as that in the uncorrelated Korringa relation, suggesting that there does not exist the strong spin fluctuation of Ru d-spins. The property of the superconducting state was investigated by using Ru NQR. We observed the Hebel-Slichter peak just below T c and the exponential decrease in 1/T1 indicating that this superconductivity has an ordinary s-wave character. The effect of Al substitution for Ru was also studied by NMR and NQR.