It seems, at first, an unlikely reason to decide to live abroad after retirement. But some older Americans apparently have concluded that the only way they can afford to travel as widely as they please is to move to a foreign country where living costs are low.

Rather than retiring in the United States and struggling on a pension, they are renting or buying good but inexpensive residences abroad, according to Jane Parker of Saratoga, Calif., who is in the business of advising retirees on foreign moves. And they are taking advantage of lower costs for food and other living expenses. The result: "If you live on a lower budget, you have money left over to travel elsewhere."

On second thought, it's not such a bad reason after all.

Parker has found that the people who manage best in a new home in a new land are those with "a sense of adventure. They are looking for something new and interesting in their lives." Not surprisingly, they also are the sort of people who want to have enough extra money in retirement to keep exploring the world.

Parker -- a retired schoolteacher who, with her husband, has invested in a place in the Algarve region of southern Portugal -- is founder of a tour company called Retirement Explorations. Each year she leads groups of retirees or prospective retirees to such warm-weather destinations as Costa Rica, Portugal, Spain and Mexico. There she schedules seminars with local lawyers, real

estate sales people, doctors, government officials and Americans already living abroad.

Parker's idea is to combine a pleasure tour with guided fact-finding for Americans who are considering a foreign home. No one should take such an enormous step without thorough research, she says. Her firm is one of several resources available to people who may be interested in a new home in retirement -- either in this country or abroad.

Many people change home towns because they are looking for a place with an agreeable year-round climate. But the biggest factor, of course, is a lower cost of living. "I don't want to pinch pennies," clients tell Parker.

Americans on a tight pension, she says, often can afford a more luxurious life style in other countries than they ever had at home. They may even be able to hire a full-time maid, cook and gardener. The old phrase "champagne living on a beer budget" is applicable here.

"Writers, artists and dabblers thrive in this enhanced, cared-for life style," Parker says. "And for the person with some chronic ailment like arthritis, it is a godsend to have inexpensive help."

Judy Furton, also a former schoolteacher, has lived with her husband in the city of Guadalajara, Mexico, for 13 years, and she says she still enjoys it. "Sorry you're having such terrible weather," she tells a Washington resident on a particularly gloomy February day. "It's 78 degrees here, the sun is shining, the flowers in bloom and never a frost."

Like Parker, the Furtons also are in the business of advising retirees. They distribute an annual informational newsletter, "Retiring in Guadalajara," and they invite visiting Americans to their home for weekly seminars on life in Mexico. A big part of both the newsletter and the seminar is letting people know how little it costs the couple to live very nicely.

On an average, the Furtons spend about $800 a month, although, they say, "we could easily live on $500 per month." They reside in a pleasant, four-bedroom, 2 1/2-bath home -- with a pool and fountain -- that they purchased for $31,000 in 1983. They hire a maid who comes four or five hours a day, five days a week. They eat out about twice a week at some of Guadalajara's fanciest restaurants -- dinner is about $5 per person, including tip. They own two Mexican-built cars. They fly back to the United States regularly to visit family and friends. And, with what's left over from their pensions, they have taken cruises and visited 34 countries.

There are drawbacks to life in a different culture, however, that many retirees may find unappealing.

Even in their own home, say the Furtons, they cannot drink the tap water, which could be an inconvenience for some. To them, "this is no hardship as pure, better-tasting water is delivered to us in 20-liter (more than five gallons) bottles for 22 cents." Telephone and mail service are poor, and some local laws may seem puzzling or irritating. For example, foreign residents cannot bring their furniture into Mexico. Furnishings must be purchased inside the country. Judy Furton confesses to not enjoying Mexican food, prefering to dine in European or Asian-style restaurants.

In addition to technical advice, Parker offers these common-sense tips to people considering retirement abroad:

Rent for at least a year before you buy a permanent home. It gives you time to decide if this is really the life for you. If not, you can return home relatively easily.

Pick a place that has convenient transportation back to your home town. Australia and New Zealand might make pleasant retirement havens, but they are a long and very costly flight away. It's a big decision whether to fly home for a birth, wedding or funeral.

Locate in a place that is convenient to good medical facilities, including an English-speaking doctor and dentist -- especially if you don't know the local language.

Don't isolate yourself from other Americans. Even though you want to explore a new culture, you will find comfort in the society of your fellow countrymen. They understand your jokes, she says.

Know what you want to get out of your new life. If, for example, concerts and theater are important to you, choose a community where they are available.

Make sure the people of the country you choose really welcome Americans as neighbors. The Costa Ricans and Portuguese are quite open to American retirees, she says, adding that the Spanish are a bit more standoffish until they get to know you.

When the time comes, consider taking out the necessary papers as a permanent resident of your new home. You don't lose your American citizenship, and you have less problems with visas and other paperwork on trips out of the country and back.

Some of the resources that can help in a search for a new retirement home are:

Retirement Explorations. Since 1980, Jane Parker has been leading fact-finding tours for retirees. She focuses on foreign communities where there is a balance of good facilities with low prices. This, of course, eliminates a number of beautiful warm-weather spots, such as Bermuda, that are expensive.

She favors Costa Rica as a place for "good living" at low cost. A couple might purchase a home in San Jose', the capital, for the cosmopolitan life and the society of some 6,000 other Americans living nearby and still be able to afford a weekend apartment at the beach. She sees southern Spanish and Portuguese coasts as possibilities for people interested in investment property. A dream villa on a hillside overlooking the sea may sell for $200,000. Other fine homes range from $50,000 to $130,000.

A 12-day tour to Costa Rica is $1,133 per person (double occupancy) from Miami and $1,278 from Los Angeles, including air fare and lodging. Departures this year are July 14 and Nov. 17. A 15-day tour of Portugal's Algarve and Spain's Costa del Sol is $2,140 from New York. Air fare, lodging and some meals are included. Departures are April 27 and Oct. 12.

At the urging of clients, she has designed an 11-day tour that takes in several of Mexico's colonial towns outside Mexico City. However, she is less enthusiastic about Mexico as a retirement haven because of the greater differences she sees between U.S. and Mexican cultures. The price is $1,043 from Houston, including air fare, lodging and several meals. The first departure is March 15 and a second is being considered for September.

Parker is investigating communities in Uruguay and Brazil for future tours.

For information: Retirement Explorations, 19414 Vineyard Lane, Saratoga, Calif. 95070, (408) 257-5378.

"Retiring in Guadalajara." The Furtons are partial to Guadalajara for a variety of reasons, among them:

-- It has a large American community with book clubs, bridge clubs, English-language churches and other home-town amenities. "Some of us are busier than before we retired," says Judy Furton.

-- The crime rate is low, and the streets are safe to walk at night. "Yes, we do have pickpockets and some home burglars, but they don't carry guns."

-- The sightseeing is excellent. Mexico "is a land of contrasts, from snow-covered mountaintops to beautiful canyons, plains, deserts, sand dunes and ocean beaches."

Plus, she says, she likes her neighbors. "Over 13 years ago, when we first rented a house here, our Mexican neighbors calmly accepted us. We were foreigners. We knew no Spanish. Yet our new neighbors were all friendly. We have always felt welcomed."

A copy of the Furtons' 1988 newsletter (12 pages) is available by airmail for $5. For $2 more (a total of $7), you will receive spring and fall updates (four pages each). The Furtons hold open house on Tuesdays from 11 a.m. to 1 p.m., answering questions about their life in Mexico. A car will pick you up at your hotel, and afterward lunch is offered at a fine Guadalajara restaurant. The price is $20 per person, and reservations are necessary.

For information: Fran and Judy Furton, Apartado 5-409, Guadalajara, Jalisco, Mexico.

RIM -- Retirement in Mexico. A Mexican company, RIM (for Retirement in Mexico), conducts monthly 13-day tours from Mexico City to several of the colonial towns outside the capital. They are Guanajuato, San Miguel de Allende, Morelia and Guadalajara and the nearby Lake Chapala area. A four-hour introductory seminar is held in Mexico City, and there is a second seminar in Guadalajara.

The emphasis is on showing Americans "the reality of the way of living in Mexico," says Efren Marquez, the manager of Barvi Tours of Los Angeles, which represents RIM. "We take people to the bank to show them the way to make investments, we take them to the hospitals, we take them to the American societies."

The cost of a tour from Mexico City is $495 or $620 per person (double), depending on the class of accommodations. The price includes lodging, seminars and ground transportation. Air fare and meals are extra. Immediate departures are scheduled for March 24 and April 21, and monthly trips are planned throughout the year.

For information: Barvi Tours, 11658 Gateway Blvd., Los Angeles, Calif. 90064, (800) 824-7102 or (213) 475-1861.

Guidebooks. Two new guidebooks are on the market aimed at helping upcoming retirees find a new home town within the United States. Both feature primarily (but not exclusively) warm-weather destinations with a generally modest cost of living.

Of the two, the most helpful is "Retirement Choices for the Time of Your Life," by John Howells (Gateway Books, $10.95 paperback). Howells has sought out dozens of communities that can provide pensioners with an inexpensive haven that also is attractive and has an inviting ambiance. And he has picked his places thoughtfully.

For example, he cites the Santa Barbara area on the coast of California, among the choicest of retirement cities in America. It is also a very expensive place to live. Howells suggests taking advantage of Santa Barbara's sophisticated amenities while living in one of the neighboring towns, where living costs are lower.

The other book is "Retirement Places Rated," by Richard Boyer and David Savageau (Rand McNally, $12.95 paperback). Its best feature is a capsule description of 131 communities, a selection that may give you some ideas you never before considered. The guide also ranks the communities according to such categories as best climate, safest streets, most services and variety of recreation -- a statistical exercise that is considerably less successful.

The top-rated retirement community, by the statistics, is the Murray and Kentucky Lake area of western Kentucky. Murray has a population of 14,000, and the nearest big city is Nashville, two hours away. It scores heavily, however, because of "low health care and housing costs, excellent access to accredited hospital, a high rating for personal safety, a good supply of physicians and medical specialists, an established public transit system, opportunities for continuing education in a mid-size state university and a huge body of inland water along its entire eastern border."

Agreeable qualities, certainly, but does the area have pizzazz? Is it really a place you would want to move to as a new home? The statistics in "Vacation Places Rated" don't answer that question. Look to Howells' "Retirement Choices" for recommendations on quality of life. By the way, Howells doesn't mention Murray.

FIRST-CLASS UPGRADE: Air Jamaica, the national carrier of Jamaica, currently is offering passengers a chance to upgrade to first class for a one-way charge of $50 above the price they pay for a coach-class ticket. The offer is good on the airline's daily flights (twice on Sunday) between Baltimore/Washington and Jamaica.

The catch is that the first-class seats are available only at the airport on the day of departure on a first-come basis. And the number of upgrades on any flight is limited.

Passengers who want to try for a round-trip upgrade can pay $100 at departure. If no first-class seats are available on the return, the second $50 will be refunded.

For information: Air Jamaica, (800) 523-5585.

TRAVEL ADVISORY: While most visitors tour the Soviet Union without problems, some difficulties can arise -- and commonly do -- because of that nation's strict customs regulations. So cautions the U.S. State Department in a recent travel advisory.

Arriving travelers should be aware, says the State Department, that "customs officials frequently confiscate religious literature they deem exceeds that required for personal use." Also subject to confiscation are anti-Soviet literature, materials considered pornographic and any undeclared currency or valuables. The latter may include travelers checks and wedding rings, according to the advisory. To be safe, declare all valuables on the arrival forms provided.

Exiting travelers should beware of attempting to take out the correspondence or other items of Soviet citizens. Also subject to question are antiques, which the State Department says are defined "as virtually anything which may be deemed of historical or cultural value purchased in the USSR." They have been seized on occasion, "even when properly documented."

American tourists accused or suspected of carrying any of these items "have sometimes been detained for several hours and subjected to interrogation, intimidation and harassment."