Two backpropagation neural network (BPNN) models were constructed to predict two historic geomagnetic storms that occurred in September 1999 and October 2003. The Disturbance storm time (Dst) indices from January 1, 1999, to December 31, 2014 (Coordinated Universal Time, UTC), were used as the training and test datasets for cross-validation in order to verify and validate the reliability and robustness of the two BPNN models, and yielded reasonable, predicted results. A large correlation coefficient (R) and low root mean square error (RMSE) were obtained, verifying the reliability of the two BPNN models. The predicted Dst indices can be provided for giving inputs in advance (i.e., any future time). Therefore, this analyzed method can serve as an excellent real-time prediction (RTP). To test the ability and possibility of the long-term prediction (LTP) obtained using the two BPNN models, the Dst indices were examined, which corresponded to two significant historic large geomagnetic storms that occurred in August 1972 and March 1989. For the both BPNN models, after evaluating their learning procedure, the time-dependence of LTP, the dependence of the predicted errors on the time period length of training datasets, and the variance by learning process, we found that they were stable models for the RTP and LTP.