Infinite molecular helices [Ag(3,3'-Py2S)]X (3,3'-Py2S = 3,3'-thiobispyridine; X- = BF4-, ClO4-, and PF6-) have been rationally constructed or induced. Crystallographic characterization (X- = BF-, monoclinic P2(1)/n, a = 8.946(3) A, b = 14.130(2) A, c = 10.124(2) A, beta = 107.83(2) degrees, V = 1218.3(5) A3, Z = 4, R = 0.0351; X- = ClO4-, monoclinic P2(1)/n, a = 8.884(1) A, b = 14.305(3) A, c = 10.110(1) A, beta = 106.78(1) degrees, V = 1230.1(3) A3, Z = 4, R = 0.0417; X- = PF6-, monoclinic P2(1)/c, a = 10.959(2) A, b = 9.808(2) A, c = 14.065(3) A, beta = 112.03(2) degrees, V = 1401.4(5) A3, Z = 4, R = 0.0442) reveals that the skeletal structure is an oblong cylindrical cationic helix consisting of alternating Ag(I) and 3,3'-Py2S species and that its counteranions are pinched in two columns inside each helix. The formation of the helical coordination polymer appears to be primarily associated with a suitable combination of the skewed conformer of 3,3'-Py2S and the potential linear geometry of the N-Ag(I)-N bond. However, the framework of the nitrate analogue [Ag(3,3'-Py2S)NO3] (monoclinic P2(1)/c, a = 8.177(2) A, b = 10.291(1) A, c = 14.771(2) A, beta = 102.19(1) degrees, V = 1214.9(4) A3, Z = 4, R = 0.0300) is a two-dimensional network consisting of an 18-membered ring unit, where each 3,3'-Py2S acts as a N,N',S- tridentate ligand connecting three tetrahedral silver(I) ions with the monodentate nitrate weakly bonded to the silver (Ag.O = 2.65(1) A) rather than acting as a counteranion. The anion exchange of [Ag(3,3'-Py2S)NO3] with BF4-, ClO4-, or PF6- has been accomplished in aqueous media. The two-dimensional networks are easily converted into the helices via the anion exchange, but the reverse anion exchange proceeds slightly. Thermal analyses indicate a relationship between the thermal stabilities and the structural properties.