This work investigates homotopy analysis method (HAM) and variational iteration method (VIM) in dealing with a nonlinear boundary value problem (NBVP) in a recent research by Azam et al. [M. Azam, M. Khan, A.S. Alshomrani, Unsteady radiative stagnation point flow of MHD Carreau nanofluid over expanding / contracting cylinder, Int. J. Mech. Sci. 130 (2017) 64-73]. By comparing HAM with VIM, it is seen that these are very effective for solving strongly nonlinear problems