<p>We embrace the notions of <i>m</i>-dependence and Markov chains in the setup of copulas to derive new families of copulas that generate <i>m</i>-dependent Markov chains. We characterize, in general, the copula of an <i>m</i>-dependent Markov chain, providing necessary and sufficient conditions for a copula to generate <i>m</i>-dependent Markov chains using the theory of nilpotent operators on separable Hilbert spaces. We also provide central limit theorems for estimates of the population mean and variance of functions of the <i>m</i>-dependent Markov chains.</p>