It claims lineage to the historical party of the same name which was active between 1861 and 1929 and which advocated for the Croatian state right, a right to self-determination at the time when Croatia was part of Austria-Hungary and Kingdom of Yugoslavia.
There were other briefly active splinter parties with the same name in the early 20th century which often changed forms and merged with each other but were eventually all disbanded by 1929.
In addition, some of these parties also operate similarly named branches in Bosnia and Herzegovina, usually on a nationalist platform promoting interests of Bosnian Croats and regularly running in the Bosnian general elections.
Because of this the name is regarded as a singular in Croatia (literally "Croatian Party of Right"), but commonly appears in English in the plural form, probably to distinguish it from the English term "Right" which is generally used for right-wing ideology.
Nevertheless, both historical and contemporary parties carrying the name are considered representatives of the conservative, nationalist, or even far-right side of the political spectrum.