The equilibrium correlation functions have been calculated for a high‐temperature plasma with enough accuracy to yield the thermodynamic functions to second order in terms of the plasma parameter. First, the classical solutions have been obtained for a two‐component plasma and a many‐component plasma and compared with the results for an electron gas in a uniform positive background. Second, the convergent solutions have been obtained starting with the quantum Bogoliubov‐Born‐Green‐Kirkwood‐Yvon (BBGKY) hierarchy. In the calculation, exchange effects as well as the Heisenberg effect have been taken into account. Also some corrections of the quantum BBGKY hierarchy concerning the symmetry properties have been given.