This article deals with prediction of turbulent flows in ducts of noncircular cross sections and, in particular, assessment of the performance in such flows of two very different models of turbulence. One model is of the two-equation, eddy-viscosity type, which is used in conjunction with a non-linear stress-strain relationship. The other is a complete Reynolds-stress transport closure that involves the solution of a differential transport equation for each of the six components of the Reynolds-stress tensor. The flows considered are characterized by the presence of secondary motions that are largely driven by the turbulence anisotropy and whose prediction remains a severe challenge to turbulence closures. Data from several experiments involving such flows are used here to assess the overall performance of the two models. It is found that the two models yield very similar results that are also of adequate engineering accuracy—an outcome that argues in favor of the use of the nonlinear two-equation model in practical computations.