We acknowledge that people with rare conditions constitute a group with a specific social identity and seek to understand what the implications of this acknowledgement are either in the stigmatization or emancipation of these individuals. We base ourselves on the observation that many people who are said to have rare conditions are told that their symptoms constitute a "rare disease," without specifying which illness it might be. And, in this respect, many people with rare conditions are considered "handicapped," people with "learning difficulties," or are given many other labels that are not always socially well accepted. This article is structured around three analytical standpoints, basing ourselves on Stuart Hall, Axel Honneth and Annemarie Jutel. Initially, we discuss the construction of the social identity of people with rare conditions based on Hall's definition of the "identity crisis." We then examine the identity of people with rare conditions from the perspective of the theory of justice as recognition, especially in relation to what Honneth refers to as "reciprocal recognition." Lastly, we highlight some of the specificities of the demands for recognition of people with rare conditions - albeit without a diagnosis - basing our study on the sociology of diagnosis from the standpoint of Annemarie Jutel.