Trifluoromethansulfonate of silver(I), AgSO3CF3 (abbreviated AgOTf), extensively used in organic chemistry, and its fluorosulfate homologue, AgSO3F, 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 (R (3) over bar space group, No. 148) with a = b = 5.312(3) angstrom and c = 32.66(2) angstrom, while AgSO3F crystallizes in a monoclinic system in the centrosymmetric P2(1)/m space group (No. 11) with a = 5.4128(10) angstrom, b = 8.1739(14) angstrom, c = 7.5436(17) angstrom, and beta = 94.599(18)degrees, 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 F-19 NMR spectrum of AgSO3F. 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. AgSO3F exhibits an unusually low melting temperature of 156 degrees 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. AgSO3F decomposes thermally above 250 degrees C, yielding mostly Ag2SO4 and liberating SO2F2. AgOTf is much more thermally stable than AgSO3F; it undergoes two consecutive crystallographic phase transitions at 284 degrees C and 326 degrees C followed by melting at 383 degrees C; its thermal decomposition commences above 400 degrees C leading at 500 degrees C to crystalline Ag2SO4 and an unidentified phase as major products of decomposition in the solid state.