Categorical functional data represented by paths of a stochastic jump process are considered for clustering. For paths of the same length, the extension of the multiple correspondence analysis allows the use of well-known methods for clustering finite dimensional data. When the paths are of different lengths, the analysis is more complex. In this case, for Markov models we propose an EM algorithm to estimate a mixture of Markov processes. A simulation study as well as a real application on hospital stays will be presented.