Large language models, such as ChatGPT, achieve amazing performance on various language processing tasks. However, they can also be exploited for improper purposes such as plagiarism or misinformation dissemination. Thus, there is an urgent need to detect the texts generated by LLMs. One type of most studied methods trains classification models to distinguish LLM texts from human texts. However, existing studies demonstrate the trained models may suffer from distribution shifts (during test), i.e., they are ineffective to predict the generated texts from unseen language tasks or topics which are not collected during training. In this work, we focus on ChatGPT as a representative model, and we conduct a comprehensive investigation on these methods’ generalization behaviors under distribution shift caused by a wide range of factors, including prompts, text lengths, topics, and language tasks. To achieve this goal, we first collect a new dataset with human and ChatGPT texts, and then we conduct extensive studies on the collected dataset. Our studies unveil insightful findings that provide guidance for future methodologies and data collection strategies for LLM detection.