This paper analyses extreme meteorological droughts in the territory of the Pannonian Basin in central and southeastern Europe. Droughts are treated from an agricultural perspective as periods of consecutive days with very little or no rainfall at all. By using data from the historical period 1981-2010, time intervals longer than 20 days with less than 3 mm per day during the growing season April-September are examined to determine theoretical and empirical distributions of their number and durations. Related discrete stochastic process of extremes is analysed by the Zelenhasic-Todorovic (ZT) method, successfully applied in hydrology and meteorology (e.g., peak flows, low flows, meteorological droughts, etc.). The method is applied to 52 locations across Pannonia Basin. At each location, the Poisson distribution is determined for the number of droughts, exponential distribution for the duration of droughts, and double exponential distribution for the duration of the (annually) longest droughts. To validate the quality of modelling and the results obtained, standard statistical goodness of fit tests are used. Historical data from the period 1981-2010 indicate that the central and northern part of Hungary and the entire territory of Vojvodina Province in the north of Serbia experienced the longest droughts, on average 55-60 days. In statistical terms, across Pannonia Basin once in 100 years drought may occur with an average duration of 56 days. Theoretically longest 100-year droughts could be expected in the northern part of Hungary (up to 70 days), the eastern part of Romania (up to 68 days), and Serbia (up to 69 days). The 2-year droughts are on the average duration of 3 weeks. Generated maps of the longest droughts in the basin may help to reduce agricultural risks due to global warming and other negative impacts of climate change.