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The high computational complexity of existing joint tracking and classification (JTC) algorithms hampers their application. After presenting a new description of the JTC problem--simultaneous tracking and classification (STC) instead of JTC, we derive two STC algorithms in both exact and approximate forms by applying Hayes' rule to the target state probability density function (pdf) and target class probability mass function (pmf) simultaneously under the assumption that the kinematic and attribute measurement processes are conditional independent. The mutual information exchange between tracker and classifier of the proposed STC algorithms is introduced by defining the simultaneous pdf-pmf of target state and class, the dependence of kinematic measurement on target class, the dependence of attribute measurement on target state and target model, class-dependent kinematic model sets, and class-dependent flight envelopes, etc. The proposed STC algorithms have four distinctive features. First, they have a modularized structure, i.e., they explicitly integrate a multiple-model filter and a Bayesian classifier. Second, the approximate versions, which follow easily from the proposed STC algorithms thanks to their modularized structure, have a closed form with a lower computational complexity and are more suitable for real-time applications. Third, the proposed exact STC algorithms are derived without the hidden approximation made in some existing multiple-model based JTC algorithms. Fourth, one of the proposed STC algorithms has the potential to further reduce the computational load since it has no redundant motion models. Simulation results suggest that the proposed STC algorithms provide a hopeful solution to a class of STC problems.