The structural and magnetic properties of (Cr, Mn, Fe)/Ag monatomic multilayers with the tetragonal L1 0 ordered structure in paramagnetic, ferromagnetic, and three antiferromagnetic states are studied by means of the self-consistent full-potential linearized augmentedplane-wave method. By means of total-energy minimization, the lattice constants for their ground states are estimated. It is found that L1 0 ordered Cr/Ag has an AF1-type antiferromagnetic ground state with a large local moment of 3.30µ B at the Cr site, L1 0 ordered Mn/Ag has an AF2-type antiferromagnetic ground state with a large local moment of 3.63µ B at the Mn site, and the L1 0 ordered Fe/Ag monatomic multilayer has a ferromagnetic ground state with an enhanced moment of 2.75µ B at the Fe site.