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The interacting multiple model (IMM) estimator has been proven to be effective in tracking agile targets. Smoothing or retrodiction, which uses measurements beyond the current estimation time, provides better estimates of target states. Various methods have been proposed for multiple model (MM) smoothing in the literature. A new smoothing method is presented here which involves forward filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode-conditioned smoother uses standard Kalman smoothing recursion. The resulting algorithm provides improved but delayed estimates of target states. Simulation studies are performed to demonstrate the improved performance with a maneuvering target scenario. Results of the new method are compared with existing methods, namely, the augmented state IMM filter and the generalized pseudo-Bayesian estimator of order 2 smoothing. Specifically, the proposed IMM smoother operates just like the IMM estimator, which approximates N2 state transitions using N filters, where N is the number of motion models. In contrast, previous approaches require N2 smoothers or an augmented state.