Hidden Markov models were introduced in the beginning of the 1970’s as a tool in speech recognition. During the last decade they have been found useful in addressing problems in computational biology such as characterising sequence families, gene finding, structure prediction and phylogenetic analysis. In this paper we propose several measures between hidden Markov models. We give an efficient algorithm that computes the measures for left-right models, e.g. profile hidden Markov models, and briefly discuss how to extend the algorithm to other types of models. We present an experiment using the measures to compare hidden Markov models for three classes of signal peptides.