  The magnetic susceptibility of underdoped yttrium and lanthanum cuprates is
interpreted based on the self-consistent solution of the t-J model of a Cu-O
plane. The calculations reproduce correctly the frequency dependencies of the
susceptibility in YBa2Cu3O_{7-y} and La_{2-x}Sr_xCuO4 attributing their
dissimilarity to the difference in the damping of spin excitations. In
YBa2Cu3O_{7-y} these excitations are well defined at the antiferromagnetic wave
vector Q=(\pi,\pi) even in the normal state which manifests itself in a
pronounced maximum -- the resonance peak -- in the susceptibility. In
La_{2-x}Sr_xCuO4 the spin excitations are overdamped which leads to a broad
low-frequency feature in the susceptibility. The low-frequency
incommensurability in the magnetic response is attributed to a dip in the
magnon damping at Q. The calculated concentration and temperature dependencies
of the incommensurability parameter conform with experimental observations.
Generally the incommensurate magnetic response is not accompanied with an
inhomogeneity of the carrier density.
