The dynamical spin susceptibility, chi(q, omega), of the extended t-J model, which reproduces Fermi surfaces of LSCO and YBCO type of high-T(c) cuprates, has been evaluated in the slave-boson mean field approximation based on the uniform (u-) and the d-wave singlet (s-) RVB states. The calculated results show reasonable agreement with neutron scattering data for the incommensurate structure in LSCO. For the commensurate structure in 90 K YBCO, the omega-dependence shows general agreement, but the location of the strongest peak at low temperatures does not. The temperature (T) dependences of the rates, T1(-1) and T(G)-1, and the shift of NMR are consistent with experimental data in the high-doping region, while they are not in the low-doping (but superconducting) region. We propose that the sharp drop in (T1T)-1 above T(c) in the low-doping region may be due to singlet formation.