The unsteady mixed convection boundary-layer flow near the two-dimensional stagnation point on a vertical permeable surface embedded in a fluid-saturated porous medium with suction and a temperature slip effect is studied numerically. Similarity equations are obtained through the application of a similarity transformation technique. The shooting method is used to solve these similarity equations for different values of the mixed convection, wall mass suction, the unsteadiness and the slip parameters. Results show that multiple solutions exist for certain ranges of these parameters. Some limiting forms are then discussed, namely strong suction, the free convection limit, the situation when there is a large temperature slip and when the time dependence dominates.