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In the past decades, a number of research results have been reported for energy-efficient scheduling over uniprocessor and multiprocessor environments. Different from many of the past results on the assumption for task power characteristics, we consider real-time scheduling of tasks with different power characteristics. The objective is to minimize the energy consumption of task executions under the given deadline constraint. When tasks have a common deadline and are ready at time 0, we propose an optimal real-time task scheduling algorithm for multiprocessor environments with the allowance of task migration. When no task migration is allowed, a 1.412-approximation algorithm for task scheduling is proposed for different settings of power characteristics. The performance of the approximation algorithm was evaluated by an extensive set of experiments, where excellent results were reported.