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Space-air-ground integrated network (SAGIN) is a new type of wireless network mode. The effective management of SAGIN resources is a prerequisite for high-reliability communication. However, the storage capacity of space-air network segment is extremely limited. The air servers also do not have sufficient storage resources to centrally accommodate the information uploaded by each edge server. So the problem of how to coordinate the storage resources of SAGIN has arisen. This paper proposes a SAGIN storage resource management algorithm based on distributed deep reinforcement learning (DRL). The resource management process is modeled as a Markov decision model. In each edge physical domain, we extract the network attributes represented by storage resources for the agent to build a training environment, so as to realize the distributed training. In addition, we propose a SAGIN resource management framework based on distributed DRL. Simulation results show that the agent has an ideal training effect. Compared with other algorithms, the resource allocation revenue and user request acceptance rate of the proposed algorithm are increased by about 18.15\% and 8.35\% respectively. Besides, the proposed algorithm has good flexibility in dealing with the changes of resource conditions.