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Passenger screening is a critical component of aviation security systems. This paper introduces the multistage sequential passenger screening problem (MSPSP), which models passenger and carry-on baggage screening operations in an aviation security system with the capability of dynamically updating the perceived risk of passengers. The passenger screening operation at an airport terminal is subdivided into multiple screening stages, with decisions made to assign each passenger to one of several available security classes at each such stage. Each passenger's assessed threat value (initially determined by an automated passenger prescreening system) is updated after the passenger proceeds through each screening stage. The objective of MSPSP is to maximize the total security of all passenger screening decisions over a fixed time period, given passenger perceived risk levels and security device performance parameters. An optimal policy for screening passengers in MSPSP is obtained using optimal sequential assignment theory. A Monte Carlo simulation-based heuristic is presented and compared with stochastic sequential assignment and feedback control algorithms. Computational analysis of a two-stage security system provides an assessment of the total security performance.