A computational study of a nonisenthalpic premixed turbulent jet flame is described. The flame burns a homogeneously premixed stoichiometric methane-air mixture injected into a coflow of air. The enthalpy (chemical + sensible) varies because of mixing between the jet fluid and the coflow. The performance of the Bray-Moss (BM) model and three flame surface density (FSD) models is evaluated by comparing the predictions of mean velocity and temperature profiles with recent experimental data. The reaction progress variable approach, which is established for isenthalpic flames, is extended to the present nonisenthalpic flames by including mean and mean square mixture fraction equations. The joint probability density function (PDF) of the reaction progress variable and the mixture fraction is modeled in terms of two statistically independent PDFs. The time-averaged reaction rate term is modeled using the BM and the FSD models. The effects of mixing with the coflow air were found to be unimportant in the evaluation of the flame speed required for modeling the mean reaction rate term. All models yielded reasonable predictions of mean velocity. Predictions of time-averaged temperatures agree better with the thin filament pyrometry data than those of Favre-averaged temperatures. The BM and MB models provided the best agreement with the mean temperature data but the other FSD models with slight tuning of the constants could provide similar agreement as well. The results show that a simple extension of the FSD models is promising for the treatment of nonisenthalpic flames. It appears that the differences in the conceptual framework of the FSD models disappear in their implementation using basically the same turbulence properties of kinetic energy and dissipation rates.