The fully developed laminar mixed-convection flow in horizontal ducts of rectangular, circular and semicircular cross-sections has been studied using a numerical model of the governing equations of motion, subject to the Boussinesq approximation and an axially uniform heat-flux condition. Dual solutions with a two- and a four-vortex flow pattern have been observed in all cases. The rectangular geometry, with its aspect ratio and Grashof number as parameters, is posed as a two-parameter problem. In this parameter-space, the critical points where the transition between the two- and the four-vortex pattern occur, follow a tilted cusp. This is akin to the phenomenon in the Taylor problem which has been thoroughly investigated by Benjamin and co-workers in a general study of bifurcation phenomena for viscous flow problems. The bifurcation phenomenon in circular ducts, which is essentially a one-parameter problem, has features similar to that observed for the Dean problem, by Nandakumar and Masliyah.