  We present a theory of magnetic (Ni) and nonmagnetic (Zn) impurities
substituted into planar Cu sites in the normal state of underdoped cuprates
exhibiting a spin gap. Both types of impurities induce magnetic moments on
neighboring Cu sites. In the case of Ni these moments partially screen the
inherent impurity spin, resulting in an effective S=1/2 moment. The
characteristic Kondo scale is found to have a power-law dependence on the
coupling constant. We investigate the spatial shape of the impurity-induced
spin density, taking into account the presence of short-ranged AF correlations,
and calculate the ^{17}O NMR line broadening induced by impurity doping.
