An exact integral equation is found for the pair distribution function. The integral equation is of somewhat different nature from the usual ones known in the theory of classical fluids, in the point that it involves an infinite series. The Helmholtz free energy is expressed as a series expansion which may be more rapidly convergent than the usual one. It is shown that the integral equation can be derived also by means of a variational principle from the expression for the free energy. It is pointed out that the theory of classical fluids may be constructed with the knowledge of the pair distribution function alone, even if a form of the pair interaction potential is not known.