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A novel flexible tetradentate ligand 1,6-bis(4′-pyridyl)-2,5-diazahexane (L), and two title complexes, [(AgL)NO3]n(1) and [(AgL)ClO4(CH3CN]n(2) were synthesized. Complex 1 (C7H9Ag0.5N2.5· O1.5) crystallizes in the monoclinic space group P2/n with a = 0.8806(1)nm, b = 0.9043(1)nm, c = 1.0255(1)nm, β = 91.49(1)°, V = 0.8164(2)nm3, Z = 4, R = 0.0354, wR2 = 0.0795. Complex2(C16· H21AgClN5O4) crystallizes in the monoclinic space group P21/n with a = 1.4220(2)nm, b = 0.7082(1) nm, c = 1.9914(3)nm, β = 94.330(10)°, V = 1.9997(5)nm3, Z = 4, R = 0.0417, wR2 = 0.1094. There is one-dimensional infinite hinge-like cationic chain in complex 1, and a two-dimensional infinite cationic network in complex 2. The results demonstrate that counterions play important roles in the supramolecular framework construction.