This paper shows the results of a research of the application of data envelopment analysis (DEA) together with artificial neural networks (ANN) of higher education institutions in Colombia during the years 2011-2013, for the purpose of evaluating the technical efficiency of Colombian higher education institutions and subsequently carry out predictions, based on a group of management indicators. Information provided by the Ministry of National Education was used as data source. The results show that this two-stage approach provides the DEA with the predictive potential that it otherwise lacks, enhancing its evaluative qualities; this is also evident in the various research papers consulted. The results also show that 50% of the models built have correct classification rates of 64.58% and 58.33% for training and validation datasets, respectively.