In the Oliphant decision, the Court ruled that Indian tribal courts do not have inherent criminal jurisdiction to try non-Indians and may not assume such jurisdiction unless given specific congressional authorization. Historically, BIA police forces were established to maintain law and order among the native inhabitants. From 1869 until 1908, Indian police forces operated relatively freely from any central control. However, several court cases led to the passage of the Major Crimes Act of 1885, which gave Federal courts and police jurisdiction over certain criminal offenses involving Indians on the reservation. Termination of tribal existence adds another dimension to the question of jurisdiction on Indian reservations. This matter is important because it brings those Indians within the jurisdiction of the State and local courts and outside the Oliphant decision. Some experts believe that Oliphant merely establishes the jurisdiction of Federal agencies over non-Indian offenders who commit crimes against Indians on the reservations. Another group argues that the decision opens the reservation to non-Indian criminals. Cross-deputization of tribal officers (as both Indian police officers and as State or local police officers) may be a solution to the jurisdictional dispute. Eleven references are included.