Knowledge of physical properties of pure components and mixtures is essential when designing new processes or improving the efficiency of existing processes. However, mixture properties at the physical conditions relevant to the process are hardly ever available. Computer power has increased considerably over the last years. Thus, it is possible to exploit computationally demanding methods like molecular simulation to predict physical properties. This is particularly attractive at conditions where real experiments are expensive or impracticable. In this thesis, Monte Carlo molecular simulation was used to predict vapour-liquid equilibria of binary and ternary mixtures. This work concentrated on the convenience of the simulation method and on the extent to what experimental data can be reproduced. The simulation method that was in the centre of interest is Gibbs-Duhem integration. Gibbs-Duhem integration implies the numerical integration of a Clapeyron differential equation describing the phase-coexistence line. Numerical integration of the Clapeyron equation requires an initial vapour-liquid coexistence point and an initial value for the integrand. Different methods to compute these boundary conditions with Monte Carlo molecular simulation were investigated, assessed, and improved. In order to perform molecular simulation, the interactions between molecules need to be quantified. These interactions are usually expressed in a so-called force field. There are many different force fields available for individual components. These force fields differ in mathematical complexity, physical significance, and transferability of the parameters. The importance of the choice of a proper force field was stressed. Conventional Gibbs-Duhem integration is a very inefficient method. In this thesis, Gibbs-Duhem integration was combined with advanced simulation and analysis techniques. The resulting advanced Gibbs-Duhem integration method provides more smooth simulation results and is faster than the conventional method. The method enables one to predict a whole coexistence curve instead of only individual coexistence points at predetermined integration steps. The advanced Gibbs-Duhem integration method was applied to a number of binary and ternary systems. In general, the agreement between simulation results and experimental data was good. Notwithstanding the convenience of the advanced Gibbs-Duhem integration method, the variety of physically unrealistic force fields published in literature currently limits the application of the method for industrial purposes.