To assess the jurisdictional void on Indian reservations following the Supreme Court decision, this project first reviewed Indian treaties, legislative policies in the 19th and 20th centuries, and executive branch opinions on non-Indian jurisdiction. Case law was examined to determine the validity of the Court's assumption that tribal criminal justice over non-Indians was inconsistent with their tribal status. The study concluded that the denial of tribal jurisdiction over non-Indians is a political question that should be resolved by Congress, not the courts. Information on the law enforcement difficulties encountered by tribes since 1978 was collected through visits to 12 reservations and questionnaires sent to over 200 active tribal governments. Analysis of this data indicated that the Oliphant decision has created serious gaps in law enforcement on reservations with non-Indian populations. Because most reservations have ceased all criminal enforcement against non-Indians and no other agency has assumed responsibility for these crimes, unregulated non-Indian crime has increased, particularly traffic offenses. The tribal justice systems have become confused, and tribal police morale is low. Economic problems have resulted from the loss of fines and Federal subsidies for tribal police. Short-term remedies adopted by tribes include cross-deputization of tribal police as county or State officers, recodification of certain criminal offenses as civil offenses, and treaty provisions which exclude non-Indians from the reservation. The report proposes that the Secretary of the Interior recognize tribal jurisdiction over non-Indian crimes committed on the reservation on the basis of individual tribe petition. Legislation could allow non-Indians to appeal a tribal court decision to Federal magistrates, Federal district court, or an Indian circuit court. Agreements with county and State authorities could provide temporary relief to jurisdictional problems. The appendixes contain the project's quarterly reports to LEAA and the survey questionnaire. Footnotes are provided.