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This paper provides a comparative study of the Variational Iteration Method (VIM) and the Adomian Decomposition Method (ADM) to obtain analytic approximations of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. An excellent agreement is observed between the series solutions for the velocity field obtained by these two methods. This comparison is bench-marked against a numerical solution. Furthermore, the VIM has an advantage over ADM that it solves the nonlinear problems without using the Adomian polynomials.