Splitting and combination are two important events of group target motion. However, the existing tracking approaches for group target splitting and combination events suffer the problems of high-computational cost and low accuracy. Under the random finite set framework, with target extent modeled by random matrix, the algorithms for group target splitting and combination tracking based on δ-generalized labeled multi-Bernoulli filter are researched. Three classical splitting modes of group target are discussed. With appropriate splitting criteria developed, e.g., the setting of the splitting gate, the chosen of the splitting dimension, the compensation of the subgroup's centroid position, and so on. According to the characteristics of each mode, the efficiency and the accuracy of the algorithm for group target splitting event are improved. The group combination approach is derived, where the representation of labels under the tack complicatedly changed condition, e.g., the group splitting and combination events jointly exist are given. With the velocity combination criterion established according to the target motion trend, a decreased sensitivity of the algorithm for target splitting event is avoided. The results show that the proposed algorithms have improved the tracking performance for group target splitting and combination events.INDEX TERMS δ-generalized labeled multi-Bernoulli, group target tracking, splitting, combination, gamma Gaussian inverse Wishart.