The magnetic properties of transition-metal dimers on Ag(001) are calculated in the local-spin-density approximation by means of a Korringa-Kohn-Rostoker Green's function technique. It is shown that many transition metals which are nonmagnetic in their bulk form are magnetic as dimers on the Ag(001) surface. The surface-dimer interaction is studied by comparing the magnetic moments of supported and free dimers. The increased sp-d hybridization with the substrate strongly decreases the magnetic moments of 4d and 5d dimers in comparison with the 3d ones. However, for these series magnetic dimers with large moments also exist.