For most real-world data streams, the concept about which data is obtained may shift from time to time, a phenomenon known as concept drift. For most real-world applications such as nonstationary time-series data, concept drift often occurs in a cyclic fashion, and previously seen concepts will reappear, which supports a unique kind of concept drift known as recurring concepts. A cyclically drifting concept exhibits a tendency to return to previously visited states. Existing machine learning algorithms handle recurring concepts by retraining a learning model if concept is detected, leading to the loss of information if the concept was well learned by the learning model, and the concept will recur again in the next learning phase. A common remedy for most machine learning algorithms is to retain and reuse previously learned models, but the process is time-consuming and computationally prohibitive in nonstationary environments to appropriately select any optimal ensemble classifier capable of accurately adapting to recurring concepts. To learn streaming data, fast and accurate machine learning algorithms are needed for time-dependent applications. Most of the existing algorithms designed to handle concept drift do not take into account the presence of recurring concept drift. To accurately and efficiently handle recurring concepts with minimum computational overheads, we propose a novel and evolving ensemble method called Recurrent Adaptive Classifier Ensemble (RACE). The algorithm preserves an archive of previously learned models that are diverse and always trains both new and existing classifiers. The empirical experiments conducted on synthetic and real-world data stream benchmarks show that RACE significantly adapts to recurring concepts more accurately than some state-of-the-art ensemble classifiers based on classifier reuse.