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Recent advancements in Generative Adversarial Networks (GANs) enable the generation of highly realistic images, raising concerns about their misuse for malicious purposes. Detecting these GAN-generated images (GAN-images) becomes increasingly challenging due to the significant reduction of underlying artifacts and specific patterns. The absence of such traces can hinder detection algorithms from identifying GAN-images and transferring knowledge to identify other types of GAN-images as well. In this work, we present the Transferable GAN-images Detection framework T-GD, a robust transferable framework for an effective detection of GAN-images. T-GD is composed of a teacher and a student model that can iteratively teach and evaluate each other to improve the detection performance. First, we train the teacher model on the source dataset and use it as a starting point for learning the target dataset. To train the student model, we inject noise by mixing up the source and target datasets, while constraining the weight variation to preserve the starting point. Our approach is a self-training method, but distinguishes itself from prior approaches by focusing on improving the transferability of GAN-image detection. T-GD achieves high performance on the source dataset by overcoming catastrophic forgetting and effectively detecting state-of-the-art GAN-images with only a small volume of data without any metadata information.