Markov copulae (MCO) provide a tool to construct a multivariate Markov process whose components (margins) are prescribed Markov processes. In this talk, first some theoretical result regarding Markov copulae will be presented. Then, an application of MCO to valuation and hedging of credit index derivatives will be given, and it will be illustrated by nice calibration results. This is a joint work with Tomasz Bielecki and Andrea Vidozzi.