Pseudoensembles are formulated to conduct Monte Carlo simulations of phase coexistence in multicomponent systems. It is shown that this approach can be applied to different types of ensembles. In contrast to the conventional Gibbs ensemble that performs flash-type calculations, pseudoensembles can also be designed to perform bubble-point and dew-point calculations. It is also shown that pseudoensemble simulations provide some connections between histogram reweighting techniques, Gibbs ensemble simulations, Gibbs-Duhem integrations, and thermodynamic integrations. In particular, pseudoensembles naturally lead to the formulation of Gibbs-Duhem integrations. The methods proposed here are validated by simulating vapor-liquid phase equilibrium of model binary mixtures.