We report on a systematic study based on the full-potential linearized augmented-plane-wave method for 3d transition metals (Ti, V, Cr, Mn, Fe, Co, Ni) as monolayers on the Ag(001) surface. For all systems we find a ferromagnetic solution and in most cases also an antiferromagnetic one, both partly with very large magnetic moments. By a total energy analysis we show that V, Cr, and Mn overlayers favour the c(2 × 2) antiferromagnetic superstructure while Ti, Fe, Co, and Ni order in the ferromagnetic p(1 × 1) configuration.