For the first time, Cu-64 tracer measurements of ionic diffusion were performed for several copper-rich glass compositions in the CuI-As2Se3, CuI-SbI3-As2Se3, CuI-PbI2-As2Se3, CuI-PbI2-SbI3-As2Se3 and Cu2Se-As2Se3 systems. In accordance with previous a.c. impedance results and Wagner d.c. polarization measurements, it was found that pure Cu+ ion-conducting glasses (50CuI-17PbL(2)-33As(2)Se(3) and 50CuI-20PbI(2)-10SbI(3)-20As(2)Se(3)) exhibit the highest copper tracer diffusion coefficients, D-Cu, and the lowest diffusion activation energies. The values of D-Cu at room temperature are higher by 4.5-5.5 orders of magnitude than those in an As2Se3 glass. The Haven ratio, H-R, is found to be 0.52-0.61 (ternary glass) and 0.93-1.00 (quaternary glass). Short-range diffusional displacements of the iodide ions induced by the hopping Cu+ ions are also detected in the CuI-PbI2-SbI3-As2Se3 glassy system using I-129-Mossbauer spectroscopy in the temperature range of 4.2 to 305 K. The activation energy of local hopping, E(h) approximate to 0.31 eV, is very similar to that of bulk ionic conductivity (0.37 eV) and copper diffusion (approximate to 0.33 eV). In contrast to CuI-based vitreous alloys, 50Cu(2)Se-50As(2)Se(3) glass exhibits D-Cu that are two to five orders of magnitude lower, and the copper ion transport number, t(Cu+), is between 10(-3) and 10(-4) in the temperature range 140-170 degrees C.