The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.