The mixed convection over a vertical surface adjacent to a fluid saturated porous medium and having the temperature distribution T-w(x) = T-infinity + T-0 (.) (x/L)(lambda) is considered in the boundary-layer and Boussinesq approximation for the value lambda = -1/3 of the power-law exponent. It is shown that in the whole range -infinity < epsilon < + infinity of the mixed convection parameter epsilon an infinite number of solutions exist which are associated with different values of the dimensionless wall temperature gradient theta'(0) equivalent to h. These solutions are investigated analytically and numerically in detail. The effect of a thermodynamic requirement on the existence domain of the physical solutions is discussed in the context of results reported by other authors. (c) 2006 Elsevier Ltd. All rights reserved.