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This article discusses multistage processing of connections in connection-switched networks. It is assumed that the incoming connections belong to different traffic classes requiring different level of services. The latter may be enforced by various factors including the most frequently respected, that is, quality of service or security policies supported by the particular network. The general idea of multistage processing of traffic is introduced, and the connections classification task in a two-stage processing scheme is discussed in detail. Proposed classification algorithms are introduced and presented. Illustrative results of quantitative examinations of the proposed algorithms are given.