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Similarly to the joint research units, the Research Federations, which are composed of several UMR or EA, are recognized by the CNRS and several other organizations. Their aim is to pool resources (Ph.D. trainings, computing resources, scientific literature) or requests for resources sent to the local administrative authorities, and to promote joint scientific initiatives : through the organization of seminars and working groups, symposia or collaborations.

There are currently nine Research Federations which are mostly focused on mathematics.

Four other federations have a mathematics section without being mainly focused on mathematics :
- Research Federation : Fundamental Interactions (FR2687)
- Wolfgang Döblin Institute (FR2800)
- Modeling, Simulation, Fundamental Interactions (FR2914)
- Research Federation on Environment for Environmental Sustainability (FR3097)

The 920520SOSI decision of July 24, 1992 such as amended, on the organization and functioning of operational research structures, provides some interesting details on the Federative Research Structures (Federative Research Institutes and Research Federations)

List and contact details of the research federations in mathematics