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Optimal control of singularly perturbed systems with free terminal time is considered. A reduction in system order is achieved by perturbing a small scalar parameter in the system equations. Using the solution of this reduced order problem, an asymptotic series approximation method is presented for obtaining the solution to the complete problem. A backward sweep approach on the reduced model is used in determining the asymptotic series terms. Numerical results on an example show the applicability of the method.