The necessary condition for the occurrence of parallel mixed convection flow in an inclined duct is determined by employing the Boussinesq approximation. A sample case involving an inclined infinitely-wide plane channel is discussed to illustrate this condition. It is shown that, according to the necessary condition, parallel flow cannot occur in this case. Indeed, the investigated flow is the superposition of a parallel streamwise flow and a secondary flow. An exponential equation of state for the fluid is assumed and the balance equations are solved analytically to determine the dimensionless velocity distribution, as well as the conditions for the occurrence of flow reversal. © 2005 Elsevier Ltd. All rights reserved.