The Na-Au-Zn system contains the two intermetallic phases Na0.97(4)Au2Zn4 (I) and Na0.72(4)Au2Zn2 (II) that are commensurately and incommensurately modulated derivatives of K0.37Cd2, respectively. Compound I crystallizes in tetragonal space group P4/mbm (No. 127), a = 7.986(1) angstrom, c = 7.971(1) angstrom, Z = 4, as a 1 x 1 x 3 superstructure derivative of K0.37Cd2 (I4/mcm). Compound II is a weakly incommensurate derivative of K0.37Cd2 with a modulation vector q = 0.189(1) along c. Its structure was solved in superspace group P4/mbm(00g)00ss, a = 7.8799(6) angstrom, c = 2.7326(4) angstrom, Z = 2, as well as its average structure in P4/mbm with the same lattice parameters.. The Au-Zn networks in both consist of layers of gold or zinc squares that are condensed antiprismatically along c ([Au4/2Zn4Zn4Au4/2] for I and [Au4/2Zn4Au4/2] for II) to define fairly uniform tunnels. The long-range cation dispositions in the tunnels are all clearly and rationally defined by electron density (Fourier) mapping. These show only close, somewhat diffuse, pairs of opposed, <= 50% occupied Na sites that are centered on (I) (shown) or between (II) the gold squares. Tight-binding electronic structure calculations via linear muffin-tin-orbital (LMTO) methods, assuming random occupancy. of <= similar to 100% of nonpaired Na sites, again show that the major Hamilton bonding populations in both compounds arise from the polar heteroatomic Au-Zn interactions. Clear Na-Au (and lesser Na-Zn) bonding is also evident in the COHP functions. These two compounds are the only stable ternary phases in the (Cs,Rb,K,Na)-Au-Zn systems, emphasizing the special bonding and packing requirements in these sodium structures.