Target classification is of great importance for modern tracking systems. The classification results could be fed back to the tracker to improve tracking performance. Also, classification results can be applied for target identification, which is useful in both civil and military applications. While some work has been done on Joint Tracking and Classification (JTC), which can enhance tracking results and make target identification feasible, a common assumption is that the statistical description of classes is predefined or known a prior. This is not true in general. In this paper, two automatic multiple target classification algorithms, which can automatically classify targets without prior information, are proposed. The algorithms learn the class description from the target behavior history. The input to the algorithm is the noisy target state estimate, which in turn depends on target class. Thus, class description is learnt from the target behavior history rather than being predefined. This motivates the proposed two-level tracking and classification formulation for automatic multiple target classification. The first level consists of common tracking algorithm such as the Joint Probability Data Association (JPDA), the Multiple Hypothesis Tracking (MHT) or the Probability Hypothesis Density (PHD) filter. In the second level, a Mean-Shift (MS) classifier and a PHD classifier are applied to learn the class descriptions respectively based on the state estimations from the first level tracker. The proposed algorithms only require the kinematic measurements from common radar. However, feature information can be easily integrated. Besides theoretical derivations, extensive experiments based on both simulated and real data are performed to verify the efficiency of the proposed technique.