Online anomaly detection is a key technology to ensure the normal operation of rocket servo systems.However，most current methods do not consider the concept drift problem that exists when models are deployed and applied，which in turn affects the detection accuracy.Therefore，based on the generative recurrent networks，this paper proposes an online anomaly detection algorithm for servo systems.First，a deep recurrent neural network is proposed to model the input-output relationship of a servo system.The network introduces multi-layer memory cells and jump connections to improve its capability to fit the multi-scale spatio-temporal dependent properties of the data.Second，to mitigate the conceptual drift problem，online learning is introduced to make the model capable of continuous learning，but it also introduces the problem of catastrophic forgetting.Finally，to mitigate the catastrophic forgetting problem，a generative network is proposed to generate the retrospective data containing information about the overall distribution of historical data.It allows the model to learn new data distributions while avoiding forgetting information about the historical data distributions.Based on the actual rocket servo system operation data，the ablation experiments and comparative experiments are carried out.The results show that the proposed algorithm can effectively address the aforementioned problems and achieve good anomaly detection results.