Repetition is an important phenomenon in a variety of domains, such as music, computer programs and architectural drawings. A generative model for these domains should account for the possibility of repetition. We present repeated observation models (ROMs), a framework for modeling sequences that explicitly allows for repetition. In a ROM, an element is either generated by copying a previous element, or by using a base model. We show how to build ROMs using n-grams and hidden Markov models as the base model. We also describe an extension of ROMs in which entire subsequences are repeated together. Results from a music modeling domain show that ROMs can lead to dramatic improvement in predictive ability.