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A general sufficient condition for global optimality in terms of inequalities between the functions involved in the definition of the problem is developed. This condition is an extension of the sufficient condition obtained by Leitmann and Stalford  and can handle problems with constraints on the control and/or the state as well as problems with free final time. Simplified forms are obtained for the particular cases of minimum time and fixed final time problems. Simple examples which illustrate the applicability of the condition to problems with several extremal solutions and/or singular subarcs are also presented.