Application of artificial neural networks (ANNs) for modeling of vapor-liquid equilibrium in multicomponent mixtures is considered. Two novel ANN-based models are introduced, which can be seen as generalizations of the Wilson model and the NRTL model. A unique feature of the proposed approach is that an ANN approximation for the molar excess Gibbs energy generates approximations for the activity coefficients. A special case of the ternary acetic acid-n-propyl alcohol-water system (at 313.15 K) is used to illustrate the efficiency of the different models, including Wilson's model, Focke's model, and the introduced generalized degree-1 homogeneous neural network model. Also, the latter one-level NN model is compared to the Wilson model on 10 binary systems. The efficiency of the two-level NN model is assessed by a comparison with the NRTL model.