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The problem of providing efficient concurrent access for independent processes to a dynamic search structure is the topic of this paper. We develop concurrent algorithms for search, update, insert, and delete in a simple variation of binary search trees, called external trees. The algorithm for deletion, which is usually the most difficult operation, is relatively easy in this data structure. The advantages of the data structure and the algorithms are that they are simple, flexible, and efficient, so that they can be used as a part in the design of more complicated concurrent algorithms where maintaining a dynamic search structure is necessary. In order to increase the efficiency of the algorithms we introduce maintenance processes that independently reorganize the data structure and relieve the user processes of nonurgent operations. We also discuss questions of transactions in a dynamic environment and replicated copies of the data structure.