Droughts are complex events which may impair social, economic, agricultural, and other activities of a society. The present hydroclimatological study comprises three stages. First, a Markov chain model based on annual flows at a gauging station located on the Goumlksu River (Turkey) is utilized. Second, a critical drought analysis is conducted. Third, the influences of the North Atlantic Oscillation (NAO) on the probability distribution functions (PDFs) of critical droughts have been documented. Drought duration is used as a key parameter in the Markov chain model. As the model degree should be defined prior to applying a Markov chain model to a series of observations, a model degree of first order has been selected according to the results of the Akaike information criteria and Bayesian information criteria. The exact PDFs of the critical drought duration in a finite sample that follows the first-order Markov chain have been determined by the enumeration technique. The critical drought duration is the possible maximum duration likely to occur over the economic life of any water resources system. The expectations of the critical drought duration are provided for different transitional probabilities. The influences of NAO on the PDFs of critical droughts have been examined for two opposite cases; namely, the period of negative NAO index values (1936-1971) and the period of positive NAO index values (1972-2000). The results of this analysis clearly indicate that NAO series have quantifiable influences on the transition probabilities and expectation of the critical drought duration. As a result, the probability distribution functions obtained for various critical drought durations in the observations of the Goumlksu River may be implemented as a robust tool to determine a design value with the concept of risk.