An analysis is carried out to investigate the steady two-dimensional stagnation-point flow of a water based nanofluid over an exponentially stretching/shrinking sheet in its own plane. Using a similarity transformation, the governing mathematical equations are transformed into coupled, nonlinear ordinary differential equations which are then solved numerically for three types of nanoparticles, namely copper (Cu), alumina (Al2O3), and titania (TiO2) in the water based fluid with Prandtl number Pr = 6.2. The skin friction coefficient, the local Nusselt number and the velocity and temperature profiles are presented graphically and discussed. Effects of the solid volume fraction phi and the stretching/shrinking parameter lambda on the fluid flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique. The range of the parameter lambda where the similarity solution exists for the steady stagnation-point flow over an exponentially stretching/shrinking sheet is larger compared with the linear stretching/shrinking case. (C) 2012 Elsevier Ltd. All rights reserved.