The two-dimensional equilibrium theory of isothermal current-carrying three-species plasmas is evaluated. That theory allows a first step to investigate self-consistently the influence of realistic oxygen ion admixtures on the equilibrium structure of two-dimensional models of the Earth's quiet magnetotail. The equations are solved explicitly in the tail approximation. The results are discussed both in view of possible observational implications and in view of the consequences for theoretical studies on the structure and stability of the Earth's magnetotail. ¿ American Geophysical Union 1989