Markov type models are often used to describe the occurrence of daily rainfall. Although models of Order 1 have been successfully employed, there remains uncertainty concerning the optimum order for such models. This paper is concerned with estimation of the optimum order of Markov chains and, in particular, the use of objective criteria of the Akaike and Bayesian Information Criteria (AIC and BIC, respectively). Using daily rainfall series for five stations in Nigeria, it has been found that the AIC and BIC estimates vary with month as well as the value of the rainfall threshold used to define a wet day. There is no apparent system to this variation, although AIC estimates are consistently greater than or equal to BIC estimates, with values of the latter limited to zero or unity.The optimum order is also investigated through generation of synthetic sequences of wet and dry days using the transition matrices of zero-, first- and second-order Markov chains. It was found that the first-order model is superior to the zero-order model in representing the characteristics of the historical sequence as judged using frequency duration curves. There was no discernible difference between the model performance for first- and second-order models. There was no seasonal variation in the model performance, which contrasts with the optimum models identified using AIC and BIC estimates.It is concluded that caution is needed with the use of objective criteria for determining the optimum order of the Markov model and that the use of frequency duration curves can provide a robust alternative method of model identification. Comments are also made on the importance of record length and non-stationarity for model identification