Equilibrium properties of a two‐dimensional guiding center plasma are reinvestigated in detail by means of the BBGKY hierarchy. A new equation of state is presented and compared with the results of the Monte Carlo simulation and the correlation energy is computed. A heuristic generalization of the the dispersion relation is investigated by means of different truncation schemes of the hierarchy. Analytical and numerical results support the appearance of periodic states for a neutral system in an unbounded domain at a moderately high value of the coupling parameter &ggr;c∼8.