  The magnetic excitation spectra in the vicinity of the resonant peak, as
observed by inelastic neutron scattering in cuprates, are studied within the
memory-function approach. It is shown that at intermediate doping the
superconducting gap induces a double dispersion of the peak, with an anisotropy
rotated between the downward and upward branch. Similar behavior, but with a
spin-wave dispersion at higher energies, is obtained for the low-doping case
assuming a large pairing pseudogap.
