In this paper, we discuss the use of some representation results for double martingales to value and hedge contingent claims in a Markovian regime-switching market. A set of N Markov jump assets is introduced to complete the Markovian regime-switching market. Using a representation for double martingales, we justify the completeness of the enlarged market. An equivalent martingale measure, or price kernel, in the enlarged market is then identified by a measure change. The option pricing formula and the hedging portfolio in the enlarged market is also discussed. Markovian regime-switching marketsdouble martingalesmartingale representationmarket completionmarked point processes.