We present molecular dynamics simulations of equilibrium clusters in two-dimensional Lennard-Jones (6-12) gas near the gas-liquid coexistence curve and in the overcritical region. Different cluster selection criteria are considered. The influence of cluster types on nonideal gas properties and the characteristics of relaxation to equilibrium for clusters are discussed. The radial distribution function near the critical point and the dependence of binding energy per cluster particle on number of particles in the cluster are calculated.