This investigation is concerned with the numerical calculation of multiple solutions for a mixed convection flow problem in horizontal rectangular ducts. The numerical results are interpreted in terms of recent observations by Benjamin (1978a) on the bifurcation phenomena for a bounded incompressible fluid. The observed mutations of cellular flows are discussed in terms of dynamic interchange processes. Each cellular flow may be represented by a solution surface in the parametric space of Grashof number Gr and aspect ratio y, which is delimited by stability boundaries. Such a stability map has been generated for each type of cellular flow by a series of numerical experiments. Once these boundaries are crossed one cellular flow mutates into another via a certain dynamical process. Although the nature of the singular points on this map have not been determined precisely, a plausible general structure of the cellular flow exchange process emerges from this map with several features in common with the Taylor Couette flow. The primary modes appear to exchange roles via the formation of tilted cusp. Other salient features such as primary mode hysteresis and quasi critical range for cellular development appear to be present. However no anomolous modes have been observed.