In the intermetallic compound YFe₂, the metallic hyperfine field at the Y nucleus, as measured by ⁸⁹Y NMR spectroscopy, is affected by the substitution of one or more neighbour Y atoms by different rare-earth impurities. In order to understand the underlying mechanisms for the transferred hyperfine interaction, we have performed first-principles calculations, within the local spin-density theory, for embedded clusters representing a Y atom and its vicinity in the compounds Y_1-xR_xFe₂ (R=Gd, Tb, Ho, Tm or Lu) and Y_1-xGd_xNi₂. The contact magnetic hyperfine field and the dipolar field were obtained; the resulting total held was found to increase with the spin of the rare-earth impurity. Orbital hyperfine fields were not considered. The contact transferred field was found to arise from direct polarization of the s electrons by the rare-earth spin.