Legitimists
Affected by sinistrisme, few conservatives explicitly called themselves right-wing during the Third Republic as it became a term associated with the counter-revolution and anti-republican feelings and by the 1900s was reserved for reactionary groups. Those Legitimists who had rallied to the Republic in 1893, after Chambord's death ten years before still called themselves "Droite constitutionnelle" or "républicaine" (Constitutional or Republican Right). However, they changed their name in 1899 and entered the 1902 elections under the name "Action libérale" (Liberal Action). By 1910, the only group which openly claimed descent from the right-wing gathered only nostalgic royalists and from 1924 on the term right-wing practically vanished from the parliamentary right's glossary.
Libertarianism
Critics such as Corey Robin describe right-libertarianism as fundamentally a reactionary conservative ideology, united with more traditional conservative thought and goals by a desire to enforce hierarchical power and social relations:Conservatism, then, is not a commitment to limited government and liberty—or a wariness of change, a belief in evolutionary reform, or a politics of virtue. These may be the byproducts of conservatism, one or more of its historically specific and ever-changing modes of expression. But they are not its animating purpose. Neither is conservatism a makeshift fusion of capitalists, Christians, and warriors, for that fusion is impelled by a more elemental force—the opposition to the liberation of men and women from the fetters of their superiors, particularly in the private sphere. Such a view might seem miles away from the libertarian defense of the free market, with its celebration of the atomistic and autonomous individual. But it is not. When the libertarian looks out upon society, he does not see isolated individuals; he sees private, often hierarchical, groups, where a father governs his family and an owner his employees.