We propose a method to classify faint objects from digital astronomical images based on a layered feedforward neural network which has been trained by the backpropagation procedure (Werbos 1974). An "academic" example showing that artificial neural network method behaves as a Bayesian classifier is discussed. A comparison of the classification results obtained from simulated data by the neural network classifier and by the well-established resolution classifier (Valdes 1982a) is performed in order to assess the reliability and limitations of the neural network classifier. A similar behaviour, up to the same faintness limit to which the resolution classifier works, is found in both classifiers. The method proposed in this paper offers a clear advantage, in terms of speed, over traditional methods in the classification of large samples of data; it allows a uniform and objective classification of large amounts of astronomical data in short computing times, which is useful for the analysis of astronomical observations with high data rates.