Trifluoromethansulfonate of silver(I), AgSO(3)CF(3) (abbreviated AgOTf), extensively used in organic chemistry, and its fluorosulfate homologue, AgSO(3)F, have been structurally characterized for the first time. The crystal structures of both homologues differ substantially from each other. AgOTf crystallizes in a hexagonal system (R3 space group, No.148) with a = b = 5.312(3) Å and c = 32.66(2) Å, while AgSO(3)F crystallizes in a monoclinic system in the centrosymmetric P2(1)/m space group (No.11) with a = 5.4128(10) Å, b = 8.1739(14) Å, c = 7.5436(17) Å, and β = 94.599(18)°, adopting a unique structure type (100 K data). There are two types of fluorosulfate anions in the structure; in one type the F atom is engaged in chemical bonding to Ag(I) and in the other type the F atom is terminal; accordingly, two resonances are seen in the (19)F NMR spectrum of AgSO(3)F. Theoretical analysis of the electronic band structure and electronic density of states, as well as assignment of the mid- and far-infrared absorption and Raman scattering spectra for both compounds, have been performed based on the periodic DFT calculations. AgSO(3)F exhibits an unusually low melting temperature of 156 °C and anomalously low value of melting heat (ca. 1 kJ mol(-1)), which we associate with (i) disorder of its anionic sublattice and (ii) the presence of 2D sheets in the crystal structure, which are weakly bonded with each other via long Ag-O(F) contacts. AgSO(3)F decomposes thermally above 250 °C, yielding mostly Ag(2)SO(4) and liberating SO(2)F(2). AgOTf is much more thermally stable than AgSO(3)F; it undergoes two consecutive crystallographic phase transitions at 284 °C and 326 °C followed by melting at 383 °C; its thermal decomposition commences above 400 °C leading at 500 °C to crystalline Ag(2)SO(4) and an unidentified phase as major products of decomposition in the solid state.