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How to adjust the transmission power at each node to achieve global energy efficiency while maintaining the network connectivity, referred as power management problem, is the major target of various topology control technologies. Moreover, fault tolerance which is often modeled as 2-edge or 2-vertex connectivity is another desired feature in many applications. In this paper, we study the fault tolerant dual power assignment problem. With the assumption of dual universal transmission power levels, we aim to minimize the total number of nodes assigned to high power level such that the resultant network topology is 2-edge or 2-vertex connected. As the problems are NP-hard, we design a novel algorithm to compute nearly-optimal solutions. From the theoretical perspective, we prove that our algorithm can guarantee 3.67-approximation for both 2-edge connectivity and 2-vertex connectivity, which improves the existing best approximation algorithm. We also conduct some numerical experiments which show that results of our algorithm are at most 2 times of optimal solutions in average and have significant improvements compared to that of existing algorithm.