The steady, mixed convection boundary-layer flow on a vertical surface is considered when there is either an exponentially increasing/decreasing surface temperature with a constant outer flow or an exponentially increasing/decreasing outer flow with a constant surface temperature, characterized by the mixed convection parameter . A different behaviour is observed in aiding flow or in opposing flow, and whether the boundary condition is increasing or decreasing. An exponentially decreasing surface temperature sets up a flow at large distances driven by the outer flow with the temperature field decreasing at a rate proportional to . An exponentially increasing surface temperature gives rise to a different behaviour for aiding and opposing flow. For aiding flow and temperature field increases as . For opposing flow the solution breaks down at a finite distance from the leading edge effectively where the wall velocity goes to zero at . With an exponentially decreasing surface temperature for aiding flow the solution evolves to the free convection limit For opposing flow the solution breaks down at a finite distance from the leading edge, effectively where the wall velocity goes to zero. For an exponentially increasing outer flow the solution evolves to the forced convection limit.