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In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the specific difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the stability of the closed-loop system while employing the asymptotic small gain theorem to establish the global attractiveness property of the closed-loop system. An example is given to show that a redesign of the controller is necessary to guarantee the global robust asymptotic stability when the input unmodeled dynamics is present.