This article investigates how the engagement of patients/' organisations (POs) in research relates to the dynamics of their activism in the area of rare diseases. It traces back how certain concerned families and groups elaborated rareness as an issue of equity and social justice, gave shape to what we call a /`politics of numbers/' for stating the fact of rare diseases as a major public health problem, and promoted patients/' critical involvement in biomedical and therapeutic research as a solution for mainstreaming rare diseases in regular health systems. It then studies three Portuguese and three French POs, which point to the limits of the epidemiological notion of rareness for capturing the compounded and intersecting nature of the bio-psycho-social make-up of their conditions. It finally shows how these critics progressively lead to the emergence of an alternative politics, which we call a /`politics of singularisation/'. At the core of this politics stands a collective and ongoing profiling of conditions and patients, whose similarities and differences relates to the ubiquity of biological pathways and diseases categories. Our contention is that this /`politics of singularisation/' not only pictures a politics of illnesses which questions the rationale for nosological classifications, but also, and consequently, affects the making of social links by suggesting the simultaneous identification of individual patients and constitution of collectives to which they partake while asserting their specificities.