In recent years, clapping synchronization between individuals has been widely studied as one of the typical synchro-nization phenomena. In this paper, we aim to reveal the synchronization mechanism of clapping interactions by observing two individuals\' clapping rhythms in a series of experiments. We find that the two synchronizing clapping rhythm series ex-hibit long-range cross-correlations (LRCCs);that is, the interaction of clapping rhythms can be seen as a strong-anticipation process. Previous studies have demonstrated that the interactions in local timescales or global matching in statistical struc-tures of fl uctuation in long timescales can be sources of the strong-anticipation process. However, the origin of the strong anticipation process often appears elusive in many complex systems. Here, we find that the clapping synchronization process may result from the local interaction between two clapping individuals and may result from the more global coordi-nation between two clapping individuals. We introduce two stochastic models for mutually interacting clapping individuals that generate the LRCCs and prove theoretically that the generation of clapping synchronization process needs to consider both local interaction and global matching. This study provides a statistical framework for studying the internal synchro-nization mechanism of other complex systems. Our theoretical model can also be applied to study the dynamics of other complex systems with the LRCCs, including finance, transportation, and climate.