The eects of Lorentz force on turbulent ¯ow of conductive ¯uid are analysed within the framework of second-moment and eddy-viscosity closure models. Additional terms representing the magnetohydrodynamic interactions in the transport equations for the turbulent stress tensor and energy dissipation rate are derived in the exact form and the parts of the terms that cannot be treated exactly are then modelled. The modelling is based on the term-by-term analysis of the direct numerical simulations (DNS) of turbulent ¯ow in an in®nite plane channel subjected to transverse uniform magnetic ®eld (Noguchi, H., Ohtsubo, Y., Kasagi, N., 1998. DNS database of turbulence and heat transfer). A priori validation of the new model is presented and compared with the DNS results for the Reynolds number based on the friction velocity Re s 150 and for the Hartmann number Ha 6. The same approach is then followed to modify the the low-Re number k±e model. The new k±e model has been applied to solve the developing threedimensional ¯ow of mercury in a rectangular-sectioned duct at inlet Reynolds number Re 2 Â 10 5 , subjected over a part of its length to a magnetic ®eld with Ha 700 (corresponding to a Stuart number N 2X45). The predicted development of `M' shaped velocity pro®les shows acceptable agreement with the experiments of Tananaev (1978) and visible improvement in comparison with the eddy-viscosity model of Ji and Gardner (