A new theory which accounts for the nonconformality of intermolecular potentials is used to obtain effective potentials which represent accurately the thermodynamic properties of simple and molecular fluids. This approximate nonconformal (ANC) theory introduces a constant softness (S) to incorporate deviations in conformality between the exact angle-averaged effective potential and a potential of reference. The softness S together with the molecular size and energy determine both the intermolecular potential and the thermodynamic properties of the fluid, i.e., the second virial coefficient, B(T). The theory is applied here to the pure noble gases and their mixtures. The cross interactions in the binary mixtures are determined from suitable mixing rules. The effective potentials of these molecules and for their cross interactions are obtained and compared with accurate pair potentials available from the literature. The ANC potentials agree very well with known pair interactions, except for He, and the pure and cross virial coefficients give excellent agreement with experimental results.