Drought is the most dangerous natural disaster. It differs from the other disasters in that it occurs insidiously, its effects are revealed gradually, and it persists for a long period. Drought has huge, negative effects on both society and natural ecosystems. In this study, values from the Standardized Precipitation Index (SPI) were used to generate drought estimation models by using Artificial Neural Networks (ANN). In addition, the probability of hydrological drought was determined by using SPI values to predict Streamflow Drought Index (SDI) values with ANN. Also, the SPI and SDI were used as the meteorological and hydrological drought indices, respectively, in conjunction with Feed Forward Neural Networks (FFNN), in ANN models. For this purpose, three rainfall and three flow gauging stations located in the Yesilirmak River Basin of Turkey were selected as the study units. The SPI and SDI values for the stations were calculated in order to create ANN estimation models. Different ANN forecasting models for SPI and SDI were trained and tested. In addition, the effects of the spatial distribution of precipitation on flows were determined by using the Thiessen Method to develop the SDI prediction model. The results generated by the ANN prediction models and resulting values were compared and the performances of the models were analyzed. The combination of ANN and SPI predicted meteorological drought with high accuracy but the combination of ANN and SDI was not as good in predicting hydrological drought.