Abstract: Aiming at the problems that a single motion model is insufficient to address the diversity and maneuverability of target motion, and that point targets and extended targets may coexist and transition under specific conditions, we propose a multi-target tracking method based on the coexistence of point and extended targets using a Poisson Multi-Bernoulli Mixture filter with multiple-model (MM-GM-GGIW-PMBM). First, based on the multi-model modeling of maneuvering target within a jump Markov system, we derive the probability mass function of the target motion model. Second, we expand the multi-target state into a hybrid state representation that includes both point and extended targets, with a point target probability introduced to classify the target type. To obtain an analytical implementation, the point target is modeled as the Gaussian distribution, while the extended target is modeled as the Gamma Gaussian Inverse Wishart distribution. The multi-target posterior probability density function and motion model probabilities under the coexisting point and extended targets are then updated using the PMBM filter. Finally, the updated point target probability and motion model probabilities are computed to jointly estimate the target type, motion model, kinematic state, as well as the Poisson measurement rate and extended state of the extended target. This method overcomes the limitations of traditional random finite set-based tracking approaches, which rely on a single motion model, by enabling unified modeling and collaborative tracking of both point and extended target. Simulation results demonstrate that in multi-maneuvering target scenarios where point and extended targets coexist and may transition into each other, the proposed algorithm outperforms single-model or single-target-type tracking methods. It can accurately identify target types at each time step and simultaneously estimate the correct motion model for maneuvering targets.