We show that the differences in the magnetic properties of Ni-Pd and Ni-Pt alloys arise mainly due to relativity. In particular, we find that the local magnetic moment of Ni increases with the addition of Pd in Ni-Pd while it decreases with the addition of Pt in Ni-Pt, as found experimentally, only if relativity is present. Our analysis is based on the effects of relativity on (i) the spin-polarized densities of states of Ni, (ii) the splitting of majority and minority spin d-band centers of Ni, and (iii) the separation between s-d band centers of Pd and Pt in Ni-Pd and Ni-Pt alloys.