Markov models are currently used for printed or hand-written words recognition. The order k is a very important parameter of these models. The aim of this paper is to use model selection criteria in order to estimate the order of a Markov model. H. Akaike (1973) suggested the AIC criterion for the estimation of the order k of a parameterized statistical model, including the term k as penalization of the likelihood function. Yet, selection according to this criterion leads asymptotically to a strict overestimation of the order. That is why we suggest the use of other consistent criteria in a Markovian case: the Bayesian and the Hannan and Quinn Information Criteria. The performance of the criteria are analysed on simulated data and on a real case: a hand-written word description. We discuss the limit of these methods in relation to the number of states in the model.