Flow of a power-law fluid film on an unsteady stretching surface is analyzed by means of homotopy analysis method (HAM [1]). For real power-law index and the unsteadiness parameter in wide ranges, analytic series solutions are given and compared with the numerical results. The good agreement between them shows the effectiveness of HAM to this problem. Additionally, unlike previous studies, the value of the critical unsteadiness parameter So, above which no solution exists, is determined analytically in this paper. (c) 2006 Elsevier B.V. All rights reserved.