It is pointed our in this paper that a more appropriate description of the joint target tracking and classification (JTC) problem would be the simultaneous probability density function (pdfs) of target state and target class instead of the joint target state-class pdf. In this paper, models of different classes are combined info a unified set. The Bayesian optimal JTC algorithm based on pdfs of target state and target class is derived, which integrates a Bayesian multiple-model filter and a Bayesian classifier. Also given is a suboptimal JTC algorithm with much lesser computational complexity, which is suitable for real-time application. Simulation results reveal that the proposed JTC algorithm provides a theoretically attractive solution to a class of joint target, tracking and classification problems.