The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameterα andm the exponent of the free stream flow. It is shown that forα〉0 the solution approaches the free convection limit, and forα〈0, there is a range ofα,αs〈α〈0, over which dual solutions exist. The nature of the bifurcation atα=αs, and how the lower branch of solutions behaves asα→0− are also considered. It is established that the solution becomes singular asm→1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely whenα is of 0(1) and whenα is small. Finally it is shown that form large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parametersα andm to be deduced.