As will be documented in detail, a common feature of all the streamflow models in the literature is that they assume some known order of Markov dependency to be available prior to calibration of the model parameters. Yet the statistical methods for finding this order are subtle and perhaps may themselves need refinement. In brief, the problem of finding the minimum order of Markov dependence is a difficult one and yet one that must be faced no matter what streamflow model is selected. This study is devoted in the main to setting forth the extant statistical techniques available for this problem of determining Markov order and applying the stated techniques to finding the order of records of particular rivers in the Tucson basin. Care is taken in describing the hydrologic properties of the rivers studied, since these properties may ultimately be crucial in establishing some a priori feelings for the range of likely orders.