[en] Low-energy geometric structures and segregation patterns of Ag–Cu and Ag–Ni nanoparticles adsorbed on MgO(0 0 1) are searched for by global optimisation methods within an atomistic potential model. Sizes betwen 100 and 300 atoms are considered for several compositions. In all cases, Ag segregates to the nanoparticle surface, so that Cu@Ag and Ni@Ag core-shell arrangements are found, with off-centre cores for Ag-rich compositions. The behaviours of Ag–Cu and Ag–Ni differ at the interface with the MgO substrate. For Ag–Cu, some Cu atoms are at the interface even for compositions that are very rich in Ag, where Ag–Ni nanoparticles present an interface completely made of Ag atoms. Ag–Ni and Ag–Cu also differ concerning their geometric structures. With increasing Ag content, in Ag–Cu we find the structural sequence faulted fcc $\to <!--\; ???\; -->$ icosahedral $\to <!--\; ???\; -->$ fcc, while in Ag–Ni we find the sequence hcp $\to <!--\; ???\; -->$ faulted fcc–faulted hcp $\to <!--\; ???\; -->$ icosahedral $\to <!--\; ???\; -->$ fcc. (paper)