Relative permeabilities are complex and important rock-fluid properties of reservoirs in which multi-phase flow conditions prevail. Measuring relative permeabilities in the laboratory using cores obtained from a reservoir is a complicated, time demanding, and labour-intensive task. There has been limited success in mathematical modelling of relative permeabilities based on rocks and fluid properties due to our inability to simulate the non-linear controlling mechanisms in place. Artificial neural networks (ANNs) promise a potential avenue for implicitly incorporating the controlling mechanisms and parameters into a model that can be utilized as an effective tool for relative permeability predictions. The methodology described in this paper exploits the unique topology of ANNs for determining the two-phase (oil-water) relative permeabilities. The ANN is a universal approximator that performs non-linear, multi-dimensional interpolations. In the development stage of the ANN model, a large number of oil-water relative permeability data sets were collected from the literature. These data sets were used to train the model. In composing the architecture of the ANN, only the readily available rock and fluid properties (end-point saturations, porosity, permeability, viscosity, and interfacial tension) have been explicitly incorporated. The predictive ability of the model was tested using experimental data sets that were not used during the training stage. The results are in good agreement with the experimentally reported data. The proposed model exhibits sensitivity to several reservoir properties. The proposed ANN model has a dynamic training base that can be expanded as new data become available.