A viscosity model has been developed for both completely liquid and heterogeneous, partly crystallised slags in the Al2O3-CaO-FeO'-SiO2 system in equilibrium with metallic iron. The Urbain formalism has been modified to describe the viscosities of the liquid slag phase over the complete range of compositions and a wide range of temperatures. The Roscoe equation has been used to describe the effect of presence of solid suspension (slurry effect) on the viscosity. The parameters of the viscosity model were optimised to describe large experimental data set in the low-order subsystems, as well as in the multi-component system. The computer package FACT was used for prediction of the proportion of solids and the composition of the remaining liquid phase. The model provides a good description of the experimental data (over four thousand experimental points) in liquid phase, and liquid + solid mixtures, over the complete range of compositions and a wide range of temperatures. This model can now be used for viscosity predictions in industrial slag systems. An example of the application of the new model to slag cleaning and reduction smelting processes is given in this paper.