The electronic properties and magnetism of Ru N clusters ͑Nϭ4, 6, 10, 13, 19, 43, and 55͒ are studied using the discrete-variational local-spin-density-functional method. The bond lengths in the clusters with Nр13 are optimized, and the cluster binding energies are found to increase monotonically with the increase of cluster size. All clusters except Ru 19 are shown to have magnetic ground states. The average magnetic moments per atom for the Ru N are found to decrease rapidly with the increase of the cluster size, although small oscillation exists. The calculated moments per atom for Ru 10 and Ru 13 clusters are in good agreement with the experimental values. Multiple magnetic solutions are explored, and double magnetic solutions are found for the icosahedral (I h ) Ru 13 cluster which is used successfully to eliminate the contradiction between the previous theory and experiment on the moment of Ru 13 cluster. The electronic structures of Ru N clusters are calculated, and indicate that all clusters are metallic in behavior. The comparison between the Ru 55 cluster and the bulk counterpart indicates that Ru 55 has shown bulklike properties in the binding energy, magnetism, valence-bandwidth, and density of states. Based on electronic-structure results, the reactivity of Ru 6 , Ru 19 , and Ru 43 clusters toward H 2 , N 2 , and CO molecules is predicted. ͓S0163-1829͑96͒10927-9͔