A theory of the dynamical spin susceptibility is presented, relevant for the normal‐state magnetic response and the resonant magnetic peak in superconducting (SC) cuprates. The analysis is based on the equations of motion for spins within thet‐Jmodel and on the memory‐function representation of magnetic response. An evidence from numerical studies of the model confirms that the damping of the spin collective model is large in the normal state being due to the decay into fermionic degrees of freedom. Assuming the saturation of equal‐time correlations at lowTthis leads to the anomalous &ohgr;/Tscaling, explaining neutron scattering experiments on cuprates at low doping. In the SC phase a d‐wave SC gap leads to a sharp resonant peak with reduced intensity and downward dispersion. © 2003 American Institute of Physics