A new nonlinear near-wall turbulence model is developed to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The k-$varepsilon$-f$sub$${mu}$/, model of Park and Sung$^$(1)/ is extended to a nonlinear formulation. The stress-strain relationship is the thrid-order in the mean velocity gradients. The strain dependent coefficients are obatined from the realizability constraints and the singular behavior at large strains. An improved explicit heat flux model is proposed with the aid of Cayley-Hamilton theorem. This new model includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the f$sub$λ/ function. The model performance is shown to be satisfactory.