||The paper deals with evaluation and improvement of two recent explicit algebraic turbulent stress models (EASMs). The first model was derived by Gatski and Rumsey (2001 Closure Strategies for Turbulent and Transitional Flows ed B E Launder and N D Sandham (Cambridge: Cambridge University Press) pp 946) and the second is the one devised by Wallin and Johansson (2000 J. Fluid Mech.403 89132). These models are studied for the turbulent flow through a square duct which involves a secondary flow and significant anisotropy between the turbulent Reynolds stress tensor components. An a priori evaluation of these models is made using direct numerical simulation (DNS) results of NavierStokes equations. In order to handle wall proximity effects, a damping function is suggested. The material frame-indifference (MFI) of these models is studied using the eigenvectors of the rate-of-deformation tensor and their angular velocities. This procedure allows us to evaluate an objective vorticity tensor. For this flow, it is shown that the weak-equilibrium assumption used in the derivation of EASMs is verified, i.e. the material derivative of the anisotropy tensor b is negligeable (Db/Dt??0). Comparisons of results from EASM and from DNS shows that these models are able to predict reasonably well such flows.