Summary: Most of existing multi-target tracking (MTT) algorithms, which are rooted in random finite set theory, generally rely on two hypotheses, i.e., the single dynamic model hypothesis and the hidden Markov chain (HMC) hypothesis, and the HMC hypothesis requires the target state to conform to a Markov process and the detection process to be independent. Unfortunately, these hypotheses may not always hold at the same time in many practical situations. Therefore, it is important to study the MTT algorithms in such scenarios when the HMC hypothesis and the single dynamic model hypothesis fail simultaneously. As a result, this paper presents a multiple model MTT algorithm, which is designed to tackle the MTT problem effectively in scenarios where both hypotheses are invalid. Firstly, when the HMC hypothesis is not satisfied, an MTT algorithm was presented based on pairwise Markov chain (PMC) and the labeled multi-Bernoulli filter (PMC-LMB). Secondly, in case that both hypotheses are not met, a multiple model MTT algorithm was proposed by extending the previously presented PMC-LMB filter to multiple PMC model case. Finally, extensive simulation was done to demonstrate the efficiency of the presented algorithms.