Federated learning (FL) involves multiple distributed devices jointly training a shared model without any of the participants having to reveal their local data to a centralized server. Most of previous FL approaches assume that data on devices are fixed and stationary during the training process. However, this assumption is unrealistic because these devices usually have varying sampling rates and different system configurations. In addition, the underlying distribution of the device data can change dynamically over time, which is known as concept drift. Concept drift makes the learning process complicated because of the inconsistency between existing and upcoming data. Traditional concept drift handling techniques such as chunk based and ensemble learning-based methods are not suitable in the federated learning frameworks due to the heterogeneity of local devices. We propose a novel approach, FedConD, to detect and deal with the concept drift on local devices and minimize the effect on the performance of models in asynchronous FL. The drift detection strategy is based on an adaptive mechanism which uses the historical performance of the local models. The drift adaptation is realized by adjusting the regularization parameter of objective function on each local device. Additionally, we design a communication strategy on the server side to select local updates in a prudent fashion and speed up model convergence. Experimental evaluations on three evolving data streams and two image datasets show that \model~detects and handles concept drift, and also reduces the overall communication cost compared to other baseline methods.