The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn data-driven features, generally based upon linear operations. However, in some scenarios, such operations do not have a good performance because of their inherited process that blurs edges, losing notions of corners, borders, and geometry of objects. Overcoming this, non-linear operations, such as morphological ones, may preserve such properties of the objects, being preferable and even state-of-the-art in some applications. Encouraged by this, in this work, we propose a novel network, called Deep Morphological Network (DeepMorphNet), capable of doing non-linear morphological operations while performing the feature learning process by optimizing the structuring elements. The DeepMorphNets can be trained and optimized end-to-end using traditional existing techniques commonly employed in the training of deep learning approaches. A systematic evaluation of the proposed algorithm is conducted using two synthetic and two traditional image classification datasets. Results show that the proposed DeepMorphNets is a promising technique that can learn distinct features when compared to the ones learned by current deep learning methods.