Two compounds, [Ag(2,4′-bpy)]NO₃ (1) and [Ag(2,4′-bpy)]CIO₄ (2), were obtained from self-assembly of AgX (X = NO₃^-, CIO₄^-) with 2,4′-bipyridine (2,4′-bpy). 1 crystallizes in the orthorhombic space group Pbca, with a = 11.2884(7) Å, b = 11.3981(10) Å, c = 16.5299(13) Å, and Z = 8, while 2 crystallizes in the monoclinic space group P2_1/c, with a = 10.6361(4) Å, b = 9.9896(4) Å, c = 11.2661(6) Å, β= 98.527(4)°. and Z = 4. Both complexes consist of helical [Ag(2,4′-bpy)] chains that are surrounded by nitrate or perchlorate counterions. Adjacent helical chains are racemic. The Ag^I atom is linked to two nitrogen atoms of the 2-pyridyl and 4′-pyridyl groups from two different 2,4′-bpy ligands as well as to the oxygen atom of the counterion. In 1, another oxygen atom of the counterion is weakly coordinated to the Ag¹ atom of an adjacent chain, thus bridging the helical chains into a wavy 2-D network structure, whereas in 2, adjacent helical chains are linked by the weak ligand-unsupported metal-metal interactions, resulting in an open 2-D network with compressed hexagons as building units. The structures of 1 and 2 imply the role that counterions may play in the framework construction.