GETTING THERE: An international dispute over air rights between Peru and the United States has complicated travel between the two countries. Both Eastern and AeroPeru once had direct flights from the United States. But because the governments have been unable to complete a new bilateral agreement on service, at present most travelers fly first to Miami. From there you can fly to Panama City on Air Panama and connect with AeroPeru for the Lima flight; or fly on Cayman Airways to Grand Cayman and connect with Faucett Airlines to Lima. AeroPeru and Faucett, which have reserved space on the connecting airlines and book the Miami-Lima flights, each are offering a round-trip fare of $459 (from Miami; maximum stay 60 days, no minimum). The ticket includes one free round-trip fare to Cuzco from Lima.

However, recent travelers report sudden changes in schedules, delays and other problems. So consult a travel agent who is familiar with all airlines serving Peru, the alternate routes and current fares.

U.S. citizens do not need visas but must have valid passports and round-trip tickets.

From Cuzco, the 70-mile trip to Machu Picchu is by scenic narrow-gauge railroad. The train leaves San Pedro Station in Cuzco daily at 7 a.m., arriving at Machu Picchu's Puente Ruinas Station about three hours later ($15 round trip, including a half-hour bus ride to the ruins). Daytrippers can return on the train that departs at 5 p.m.

If you want to spend more time at Machu Picchu, and are able to reserve a room at the small Hotel de Turistas on the mountaintop ($40 single, $55 double, with continental breakfast), you can stay overnight and return to Cuzco the next afternoon after a more leisurely look at the ruins.

It is also now possible to board a bus at the Cuzco airport or at the Cuzco train station for a one-hour ride to Ollantaytambo Station, en route to Machu Picchu. At that station you board one of the narrow-gauge trains, which then completes the journey with the short bus ride to the ruins. Service on this route also begins at 7 a.m., but there are multiple departures throughout the day.

WHERE TO STAY: In Cuzco, two of the major hotels are El Dorado Inn ($40.99 single, $54 double) and Hotel Libertador Cuzco ($49.42 single, $57.80 double), without meals. The government operates a hostel where rates are as low as $4 per person for five or more in a room.

SPECIAL EVENTS: Cuzco hosts a number of song and dance festivals during June to celebrate the Indians' Incan heritage and the influence of Christianity on it. The major pageant, Inti Ramyi, takes place June 24 at the ruins of Sacsayhuaman, an Incan fortress on a hill on the city's northern outskirts. Hotels usually must be booked far in advance during this period.

CONDITIONS: The Peruvian government has recently designated certain areas of Peru "emergency zones" because of terrorist activity and drug trafficking. But these areas are located in the south-central and north-central mountains, and the U.S. State Department says tourists visiting the major archeological and historical attractions should not encounter difficulties.. (Peruvian law is "very severe" regarding drug-related offenses, according to the State Department, and arrest and prosecution are not dependent on possession of any minimum amount.) There have been sporadic terrorist actions in some urban areas, including Lima, but the State Department reports that no U.S. travelers have been directly affected.

However, visitors should take precautions against theft and pickpockets; those traveling alone should be particularly careful and not stray from well-traveled roads and paths except with a tour group or competent guide. Tourism officials in Peru, which is suffering from severe economic problems, concede that tourists may be targeted by thieves. Visitors are urged to be especially wary of small children who may grab handbags or other valuables on the street.

Americans should register upon arrival with the U.S. Embassy's Consular Affairs Section at 346 Grimaldo del Solar, Miraflores, Lima (44-3621 or 44-3921).

INFORMATION: See a travel agent or write to: Office of Tourism, Republica de Panama 3055, 15th Floor, San Isidro, Lima 27. Tourism information offices in the United States were shut down recently, but the Peruvian Consulate (805 Third Ave., 14th Floor, New York, N.Y., 212-644-2850) will answer general questions.