The principal factors that influence satisfaction with a university are analyzed in this paper. A distinction is drawn for that purpose between the factors that intervene before, during, and after the phase of university education, at all times from a graduate perspective. A sample of 9380 interviews with graduates from three separate academic courses is prepared to achieve our objective. Artificial neuronal networks are applied, with which both categorical and continuous variables may be processed, testing different network architectures (number of layers, type of learning, and algorithm). The results indicated that the variables reflecting the quality of the education received and entry into the employment market are the variables that determine satisfaction to a greater extent and less so than the motives for their choice of university course, scientific area, demographic variables, and academic records.