With the rapid progress of Large language models (LLMs) and the huge amount of text they generate, it becomes impractical to manually distinguish whether a text is machine-generated. The growing use of LLMs in social media and education, prompts us to develop methods to detect machine-generated text, preventing malicious use such as plagiarism, misinformation, and propaganda. In this paper, we introduce two novel zero-shot methods for detecting machine-generated text by leveraging the Log-Rank information. One is called DetectLLM-LRR, which is fast and efficient, and the other is called DetectLLM-NPR, which is more accurate, but slower due to the need for perturbations. Our experiments on three datasets and seven language models show that our proposed methods improve over the state of the art by 3.9 and 1.75 AUROC points absolute. Moreover, DetectLLM-NPR needs fewer perturbations than previous work to achieve the same level of performance, which makes it more practical for real-world use. We also investigate the efficiency-performance trade-off based on users’ preference for these two measures and provide intuition for using them in practice effectively. We release the data and the code of both methods in https://github.com/mbzuai-nlp/DetectLLM.