The static properties of a spin system with two species are investigated by the Monte Carlo technique. The Hamiltonian of the system is similar to the effective Hamiltonian describing nuclear spin-spin interactions under the experimental circumstances designed to produce nuclear dipolar magnetic ordering. The spin structures are determined at negative spin temperatures for various ratios, R, of the magnetic moments. The structures are of the antiferromagnetic type. For two values of R we have calculated the temperature variation of the staggered magnetization of the two species as well as components of the bulk and staggered susceptibilities. It is shown that the mean-field theory is qualitatively but not quantitatively adequate to describe the transverse and longitudinal bulk susceptibilities for the two species in the antiferromagnetic phase. The results are discussed in relation to recent nuclear-magnetic-resonance experiments on LiF and neutron scattering experiments on LiH.