The structure of the (Ag2SO4)x(AgPO3)1-x glasses is investigated with P-31 NMR magic angle spinning techniques. For x < 0.2 the sulphate modifies the phosphate, and preferentially occupies a bridging position between two PO42- end units; in the sulphate-rich glasses a substantial fraction of Ag2SO4 goes into interstitial positions; the population of end units with a non-bridging SO42- is rather small, and almost independent of composition for x > 0.1. The structural description qualitatively agrees with conductivity, acoustic attenuation, and glass transition temperature (T(g) data. In particular, a Debye-like peak associated with the Ag+ jumping is seen at 168 K in the radiofrequency acoustic absorption of the x = 0.3 glass. This suggests that silver is very mobile near the interstitial sulphates, but that its long-range diffusion is controlled by slower processes.