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Federated learning has been extensively studied and is the prevalent method for privacy-preserving distributed learning in edge devices. Correspondingly, continual learning is an emerging field targeted towards learning multiple tasks sequentially. However, there is little attention towards additional challenges emerging when federated aggregation is performed in a continual learning system. We identify \textit{client drift} as one of the key weaknesses that arise when vanilla federated averaging is applied in such a system, especially since each client can independently have different order of tasks. We outline a framework for performing Federated Continual Learning (FCL) by using NetTailor as a candidate continual learning approach and show the extent of the problem of client drift. We show that adaptive federated optimization can reduce the adverse impact of client drift and showcase its effectiveness on CIFAR100, MiniImagenet, and Decathlon benchmarks. Further, we provide an empirical analysis highlighting the interplay between different hyperparameters such as client and server learning rates, the number of local training iterations, and communication rounds. Finally, we evaluate our framework on useful characteristics of federated learning systems such as scalability, robustness to the skewness in clients' data distribution, and stragglers.