Despite recent advancements in detecting disinformation generated by large language models (LLMs), current efforts overlook the ever-evolving nature of this disinformation. In this work, we investigate a challenging yet practical research problem of detecting evolving LLM-generated disinformation. Disinformation evolves constantly through the rapid development of LLMs and their variants. As a consequence, the detection model faces significant challenges. First, it is inefficient to train separate models for each disinformation generator. Second, the performance decreases in scenarios when evolving LLM-generated disinformation is encountered in sequential order. To address this problem, we propose DELD (Detecting Evolving LLM-generated Disinformation), a parameter-efficient approach that jointly leverages the general fact-checking capabilities of pre-trained language models (PLM) and the independent disinformation generation characteristics of various LLMs. In particular, the learned characteristics are concatenated sequentially to facilitate knowledge accumulation and transformation. DELD addresses the issue of label scarcity by integrating the semantic embeddings of disinformation with trainable soft prompts to elicit model-specific knowledge. Our experiments show that \textit{DELD} significantly outperforms state-of-the-art methods. Moreover, our method provides critical insights into the unique patterns of disinformation generation across different LLMs, offering valuable perspectives in this line of research.