We describe algorithms for the recently developed Bin Monte Carlo (Bin MC) method (Fan et al., 2012) and kinetic Monte Carlo (KMC) (Ustinov and Do, 2012) to simulate binary liquid mixtures, and compare them with simulations of vapour liquid equilibria from the canonical and Gibbs MC methods. We have found that in kMC, the rule to choose a molecule to move rusts purely on the mobility, irrespective of molecular weight. In the Bin MC, the choice of a molecule to move from one bin to another bin depends on the selection of a component with equal probability. Our simulations show that the Bin MC and kMC schemes are very effective for the purpose of describing thermodynamic properties and density profiles across the vapour liquid interface, and show that the Lorentz-Berthelot (LB) mixing rule works well for subcritical systems, and to improve the description of systems having one component under supercritical condition the cross collision diameter and the cross well depth have to be modified from the LB mixing rules, which is in agreement with previous studies (for example, (Wu and Sadus, 2000)). The benefits of the kMC scheme for the direct determination of chemical potential were also demonstrated with a study of adsorption of an argon-krypton mixture on graphite. (C) 2013 Elsevier Ltd. All rights reserved.