A model is presented for the calculation of the static dielectric properties of pure and dipole-dilute bcc antiferroelectric systems. The real systems display long-range dipolar and elastic interactions, which are simulated in this paper by an effective Hamiltonian with first- and second-neighbor interactions only. The first-neighbor interaction is taken to be antiferroelectric but the second neighbors, although ferroelectrically ordered at T=0 K for the pure systems, are allowed to interact via (i) a ferroelectric or (ii) a weak antiferroelectric coupling. The cluster-variation method is used to treat this model. The results show that the dielectric properties are qualitatively different in cases (i) and (ii). We conjecture that in orthorhombic KCN the effective second-neighbor interaction is antiferroelectric. The model is also of interest for other antiferroelectric and antiferromagnetic systems.