We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface.The power law non-Newtonian fluid is considered as a lubricant.The lubrication layer is thin and assumed to have a variable thickness.The transformed nonlinear ordinary differential equation goveing the flow is linearized using quasilinearization.The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order RungeKutta method.The results are discussed to see the influence of pertinent parameters.The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.