Electronic energy spectra ͑q͒ of antiferromagnetically ordered media may display nonreciprocity; that is, the energies corresponding to Bloch states with wave numbers q and Ϫq may be different. In this paper a simple Kronig-Penney model, which includes a staggered microscopic magnetic and electric fields of the proper symmetry, is employed to estimate the magnitude of nonreciprocity effects in systems such as antiferromagnetically ordered crystals as well as periodical layered structures. ͓S0163-1829͑97͒06318-2͔