The malicious misuse and widespread dissemination of AI-generated images pose a significant threat to the authenticity of online information. Current detection methods often struggle to generalize to unseen generative models, and the rapid evolution of generative techniques continuously exacerbates this challenge. Without adaptability, detection models risk becoming ineffective in real-world applications. To address this critical issue, we propose a novel three-stage domain continual learning framework designed for continuous adaptation to evolving generative models. In the first stage, we employ a strategic parameter-efficient fine-tuning approach to develop a transferable offline detection model with strong generalization capabilities. Building upon this foundation, the second stage integrates unseen data streams into a continual learning process. To efficiently learn from limited samples of novel generated models and mitigate overfitting, we design a data augmentation chain with progressively increasing complexity. Furthermore, we leverage the Kronecker-Factored Approximate Curvature (K-FAC) method to approximate the Hessian and alleviate catastrophic forgetting. Finally, the third stage utilizes a linear interpolation strategy based on Linear Mode Connectivity, effectively capturing commonalities across diverse generative models and further enhancing overall performance. We establish a comprehensive benchmark of 27 generative models, including GANs, deepfakes, and diffusion models, chronologically structured up to August 2024 to simulate real-world scenarios. Extensive experiments demonstrate that our initial offline detectors surpass the leading baseline by +5.51% in terms of mean average precision. Our continual learning strategy achieves an average accuracy of 92.20%, outperforming state-of-the-art methods.