The approximate nonconformal (ANC) theory, successfully applied to dilute gases, is generalized to dense fluids. Monte Carlo simulations were performed for several ANC potentials, used as effective nonconformal interactions in the theory. These results were used to assess the performance of alternate equations of state (EOS). Perturbation theory illuminates the effects of nonconformality but fails to produce an EOS of ANC fluids of the needed accuracy. An accurate empirical EOS was found for supercritical fluids and used to test the applicability of the theory. EOSs were found for Lennard-Jones, two-center Lennard-Jones, linear Kihara, and square well heterodiatiomic fluids. These theoretical EOSs are in good agreement with simulation results of the same fluids. The effective potentials of the nonspherical systems are found to be state-dependent with parameters modeled by a low order virial-like series. These results give a basis for the application of the theory to real dense fluids.