In this paper, we present a first-order hard sphere perturbation theory of nonideal ternary fluid mixtures. Results are reported for total and excess thermodynamic properties of three ternary mixtures, in which size parameters of the mixture components are the same, but energy parameters differ significantly. Comparisons of theoretical predictions with accurate simulation results for mixture density, internal energy, excess Gibbs free energy, excess volume and excess enthalpy show the very good performance of perturbation theory. We have also checked the accuracy of van der Waals one-fluid theory, which uses an accurate equation of state for the pure fluids. Van der Waals one-fluid theory is successful in predicting excess properties of nearly ideal to moderately nonideal mixtures, but becomes less reliable when the mixtures become highly nonideal. In general, perturbation theory is very reliable in predicting thermodynamic properties of ternary mixtures, and is found to be more accurate than van der Waals one-fluid theory.