A gendarmerie or gendarmery is a military component with jurisdiction in civil law enforcement. The term gendarme is derived from the medieval French expression gens d'armes, which translates to "armed people".
In Overthrow, NATO will station gendarmerie in towns they control to keep the peace and stop any illegal activity. They can be spotted wearing blue uniforms. If those are killed, stability will drop in the town and more will be sent from the closest base. If there is no base with land access to the town then Stability will drop quickly. If the base is close enough they will walk, otherwise they will be sent in an offroad. The gendarmerie do not need to be physically in a town for stability to drop, if you kill them in transit it will still count for the town they are heading to.
Killing gendarmerie will also drop your local standing