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We have studied the local crystal structure and magnetic properties of new disilver layered oxides Ag2FeO2 and Ag2Ga0.98Fe0.02O2 demonstrating metallic conductivity. The 57Fe Mössbauer measurements have shown that in both structures iron ions are stabilized as Fe3+ which assumes the similarity of the formal valence distribution in (Ag2)+[(Ga,Fe)3-O2]-. The observed in spectra of Ag2Ga0.9857Fe0.02O2 the line-area asymmetry is entirely associated with the texture effects, i.e., preferred orientation of platy crystalline in the plane of sample surface. Single Zeeman pattern in the 57Fe Mössbauer spectrum of Ag2FeO2, measured at T < TN 20 K, reflects the equivalence of magnetic positions occupied by Fe3+ ions with the hyperfine field Hhf(10K) 485 kOe acting on the 57Fe nuclei which is directed perpendicular to the c-axis (parallel to the principal axis VZZ of the EFG tensor) with planar (XY)-anisotropy. The spectra of the ferrite show unusual magnetic relaxation behavior below TN, as if the long-range magnetic ordering coexisted with rapid spin fluctuations. We discuss a phenomenological Kosterlitz-Thouless model, assuming that ideal 2D planar magnet, besides spin-wave excitations, exhibits a specific non-linear excitations in a form of coupled vortex pairs with opposite helicities freely moving in a plane.