Phonation modes play a vital role in voice quality evaluation and vocal health diagnosis. Existing studies on phonation modes cover feature analysis and classification of vowels, which does not apply to real-life scenarios. In this paper, we define the phonation mode detection (PMD) problem, which entails the prediction of phonation mode labels as well as their onset and offset timestamps. To address the PMD problem, we propose the first dataset PMSing, and an end-to-end PMD network (P-Net) to integrate phonation mode identification and boundary detection, which also prevents the over-segmentation of frame-level output. Furthermore, we introduce an adapted P-Net model (AP-Net) based on an adversarial discriminative training process using labeled data from one singer and unlabeled data from unseen singers. Experiments show that the P-Net outperforms the state-of-the-art methods with an F-score of 0.680, and the AP-Net also achieves an F-score of 0.658 for unseen singers.