Our recently developed model to describe the viscosity of silicate melts is extended to describe and predict the viscosities of alkali-rich silicate melts. The model requires one additional binary parameter for each M 2 O–SiO 2 system, where M is an alkali metal, to a total of three binary parameters per binary system alkali oxide – silica. In addition to unary and binary parameters, the model requires two ternary parameters for each alumina-containing ternary system M O x –Al 2 O 3 –SiO 2 , where M O x is a basic oxide, to describe the viscosity maxima in these ternary systems due to the Charge Compensation Effect. The viscosity of multicomponent melts and of ternary melts M O x – N O y –SiO 2 , where M O x and N O y are basic oxides, is predicted by the model solely from the unary, binary and ternary parameters. The available viscosity data for the alkali-containing subsystems of the Al 2 O 3 –CaO–MgO–Na 2 O–K 2 O–SiO 2 system are reviewed. The model reproduces the experimental data for binary and ternary melts and predicts the viscosities of multicomponent melts within experimental error limits. In particular, the viscosities of glass melts and melts of importance for petrology are well predicted by the model.