This article presents a study based on evaluating different techniques to automatically recognize the basic emotions of people with Down syndrome, such as anger, happiness, sadness, surprise, and neutrality, as well as the statistical analysis of the Facial Action Coding System, determine the symmetry of the Action Units present in each emotion, identify the facial features that represent this group of people. First, a dataset of images of faces of people with Down syndrome classified according to their emotions is built. Then, the characteristics of facial micro-expressions (Action Units) present in the feelings of the target group through statistical analysis are evaluated. This analysis uses the intensity values of the most representative exclusive action units to classify people’s emotions. Subsequently, the collected dataset was evaluated using machine learning and deep learning techniques to recognize emotions. In the beginning, different supervised learning techniques were used, with the Support Vector Machine technique obtaining the best precision with a value of 66.20%. In the case of deep learning methods, the mini-Xception convolutional neural network was used to recognize people’s emotions with typical development, obtaining an accuracy of 74.8%.