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The problem of state estimation and system structure detection for discrete-time stochastic systems with parameters which may switch among a finite set of values is considered. The switchings are modeled by a semi-Markov, or Markov, chain with known transition statistics. A fixed time delay (lag) is allowed in estimation (smoothing) and detection. The optimal solutions require geometrically increasing computations and storage with time. Suboptimal solutions are proposed to alleviate this problem and simulation results are presented to illustrate the effectiveness of the proposed algorithms and the advantages of introducing a delay in processing of the observations.