A Ag-109 NMR investigation of [TeO2-R Ag-0.5]((1-x))[AgI]((x)) and [TeO2-R TlO0.5]((1-x))[AgI]((x)) glasses, involving either AgI or the (AgI)(0.75)(TII)(0.25) eutectic mixture, has been carried out. The data analysis suggests a progressive crossing from an oxy-iodide environment of Ag+ ions to a more and more iodide environment as AgI content increases. A quasi-linear dependence of the chemical shift of the Ag-109 NMR line (delta) versus the r = (x(Ag+))(AgI)/(x(Ag+))(tot) ratio indicates that a fast exchange of Ag+ ions over different sites is operating at room temperature. The decrease of the Ag-109 linewidth observed as x(AgI) increases agrees with the increase of the Ag+ ion mobility deduced from conductivity data. In the [TeO2-R TlO0.5]((1-x))[(AgI)(0.75)(TII)(0.25)]((x)) series containing the eutectic mixture, the value of delta (delta = 680 ppm) is independent of x(AgI) and close to those of alpha-AgI and beta-AgI phases.