The average chemical shifts and the distribution of the shifts about the average are obtained for CuPd, CuZn, and AgPd alloys using supercells that contain hundreds of atoms. Density functional theory and local density approximation (DFT-LDA) calculations are carried out using the order-N locally self-consistent multiple-scattering method. The DFT-LDA calculations provide reliable predictions for the chemical shifts in the alloys, but the electron spectroscopy for chemical analysis potential model does not. [S0031-9007(98)06901-4]