Title: Fairness of Federated Learning with Dynamic Participants. Abstract: The concept of fairness has widely caught the attention of Federated Learning (FL). While there are tremendous studies about various notations of fairness in FL in recent years, all of them only consider the case where the training process starts and ends at the time point for all participants. Actually, participants could be dynamic and they may join and leave the training process at different time points. However, participants who join the training process at different time points receive similar incentive benefits can be seen as a signal of unfairness. In this paper, we provide the first study on such fairness of FL for dynamic participants. First, we propose a new mathematical definition of the above fairness namely $\textit{dynamic fairness}$. Briefly speaking, an algorithm is dynamically fair and satisfies that local agents who participate in the model training longer should receive more benefits than those who participate in the process shorter. Second, we develop a simple but novel method, which could be seen as a normalized version of $\textit{Fedavg}$, and theoretically show that it is fairer than $\textit{Fedavg}$.  Moreover, we can combine our method with the previous methods in fair FL for static participants to additionally guarantee fair treatment for local agents who join the training process at the same time point by minimizing the discrepancy of benefits they receive. Finally, empirically we propose a measure for $\textit{dynamic fairness}$ and demonstrate that our method can achieve a fairer performance under our definition of fairness through intensive experiments on three benchmark datasets. 