 In the 1880s , Congress passed the Major Crimes Act , divesting tribes of criminal jurisdiction in regard to several felony crimes . In 1990 , the Supreme Court ruled in Duro v. Reina that an Indian tribe did not have the authority to try an Indian criminally who was not a member of that tribe . The following year , Congress passed a law that stated that Indian tribes , because of their inherent sovereignty , had the authority to try non @-@ member Indians for crimes committed within the tribe 's territorial jurisdiction . 
