Federated Learning (FL) is an emerging domain in the broader context of artificial intelligence research. Methodologies pertaining to FL assume distributed model training, consisting of a collection of clients and a server, with the main goal of achieving optimal global model with restrictions on data sharing due to privacy concerns. It is worth highlighting that the diverse existing literature in FL mostly assume stationary data generation processes; such an assumption is unrealistic in real-world conditions where concept drift occurs due to, for instance, seasonal or period observations, faults in sensor measurements. In this paper, we introduce a multiscale algorithmic framework which combines theoretical guarantees of FedAvg and FedOMD algorithms in near stationary settings with a non-stationary detection and adaptation technique to ameliorate FL generalization performance in the presence of concept drifts. We present a multi-scale algorithmic framework leading to $\tilde {\mathcal {O}} (\min \{ \sqrt {LT}, \Delta ^{({1}/{3})}T^{({2}/{3})} + \sqrt {T} \})$ dynamic regret for $T$ rounds with an underlying general convex loss function, where $L$ is the number of times non-stationary drifts occurred and $\Delta$ is the cumulative magnitude of drift experienced within $T$ rounds.