We address the problem of temporal unusual event detection. Unusual events are characterized by a number of features (rarity, unexpectedness, and relevance) that limit the application of traditional supervised model-based approaches. We propose a semi-supervised adapted Hidden Markov Model (HMM) framework, in which usual event models are first learned from a large amount of (commonly available) training data, while unusual event models are learned by Bayesian adaptation in an unsupervised manner. The proposed framework has an iterative structure, which adapts a new unusual event model at each iteration. We show that such a framework can address problems due to the scarcity of training data and the difficulty in pre-defining unusual events. Experiments on audio, visual, and audio-visual data streams illustrate its effectiveness, compared with both supervised and unsupervised baseline methods.