The objective of our research is first of all the development of a method for learning the transition probabilities in (possibly hidden) Markov models using imprecise probabilities, and next the application of this method to some real-life problems. The learning model used will be the imprecise Dirichlet model, an extension of the precise Dirichlet model to the theory of imprecise probabilities. Possible applications are gene-sequence alignment and pre-fetching of web pages.