We derive a new expansion method for the thermodynamic properties and correlation functions of imperfect gases. When the interparticle potential is repulsive, we obtain an alternating series of upper and lower bounds for the activity, free energy, pressure, entropy, internal energy, and for the correlation functions. These bounds are valid even if there is a transition. If the potential has an attractive part, we can obtain upper bounds for the activity, free energy, internal energy, and the correlation functions.