How many more Americans can squeeze into Europe in a single summer? Who really knows? But tourists from this side of the Atlantic seem determined to find out. For the third year in a row, Europe is anticipating a record-breaking flood of vacationers from the United States.

An estimated 6 million to 6.6 million Americans are expected to travel to Europe this year, up from 5.5 million in 1984, itself a phenomenal year. Most of the increase will be vacationers.

"It's clear that it is going to be a boom year," says Jeffrey Joseph, executive vice president of Globus-Gateway/Cosmos Tourama, a major European tour packager. "Demand is up. We see it already."

This summer is going to be "busy," says Pamela Paul, vice president of American Express Vacations, another top tour supplier. "We have seen a very strong trend to go to every part of Europe -- and to the rest of the world for that matter."

The big reasons: The continuing strength of the dollar and the affordable air fares that have made transatlantic travel a good bargain.

How long will it last?

Each spring since 1983, financial forecasters have said the dollar was due to drop at any moment -- and it didn't. This year, too, there are predictions that the dollar may finally falter; even if it does, it would have to plunge substantially before Europe becomes as costly as it was for American travelers in the late '70s.

As a result of the financial situation, in the last three years a sort of "snowballing" effect has developed, agree Paul and Joseph. Travelers returning from Europe tell their friends about the bargains, and the friends start making plans. And many Americans are even making repeat visits. Travel is up year-round, not just in summer.

The travel industry, taking the optimistic view, has prepared for another big year for transatlantic holidays. And so: travelers stopping for lunch in quaint sidewalk cafes may find, as many did in 1984, that every table in the place is occupied by other Americans. Only this summer, the wait in line to get seated could be longer.

Still, with industry spokesmen claiming that a vacation trip to Europe today is actually cheaper than it was six years ago, you may not really mind the wait.

Last year's heavy demand caught some tour firms by surprise, and they ran out of tours to sell. They don't want to make the same mistake this year. Globus/Cosmos has increased its tour capacity by 33 percent over last year. The firm could have sold 20,000 more tours in 1984, says Joseph, but had to turn customers away.

TWA's Getaway Tours, another major tour operator, expects to sell 200,000 travel packages this year, double the number sold two years ago. American Express, says Paul, has increased the number of its tours by 50 percent.

Airlines are scheduling more flights. Pan Am is flying to five additional European cities this summer -- Amsterdam, Belgrade, Bucharest, Nice and Warsaw -- and has added other nonstop flights, including daily service to Frankfurt from Washington/Dulles. Charter airlines, which are increasing service also, will again offer cheaper fares than scheduled carriers.

The biggest problem facing travelers as a result of this year's transatlantic flow will be finding a place to stay.

With the big tour companies snapping up substantially more hotel space, independent travelers -- those who don't buy package tours -- may have even more difficulty this year than last in getting a room in the hotel they want, especially in Europe's principal tourist cities. What that in mind, it is a good idea to make reservations early.

Joseph also suggests that travelers who do reserve lodging make a deposit to avoid being bumped from the hotel of their choice, particularly in popular cities. His firm and others, which do thousands of dollars of repeat hotel business, found themselves bumped on occasion last summer, despite longstanding commitments for rooms.

If large tour operators can be bumped, he says, then individual travelers without a deposit have little protection if it happens to them.

Already some travelers are finding they have had to reserve rooms at higher rates than they planned because less expensive accommodations in favorite hotels are no longer available. Deluxe rooms in such popular destinations as Rome and Venice go for similarly deluxe prices of $150 a night or more.

After the first two boom years, Europe began to build more first-class hotels to accommodate even greater numbers of American travelers, says Joseph, but the new rooms won't be ready until 1986. As a result, "1985 is the crunch year."

Nevertheless, do-it-yourself travelers shouldn't be frightened off. Comfortable rooms should be available in most cities, says Joseph. The hotels may not be centrally located or come with the private bath so many Americans prefer. But "they'll find something."

Even with the strength of the dollar, a vacation in Europe is not exactly cheap. On the other hand, it's not expensive either.

Based on what recent travelers to Europe have found, costs for food and lodging should be less than what would be expected for similar quality meals and hotels in the United States, and probably substantially less, especially in the countryside.

Less than $70 a night will get you a double room in a small, elegant hotel on the Left Bank in Paris, including continental breakfast. Pan Am's tour desk is quoting double rates below $40 a day in London in certain hotels.

The Wayfarers of West Sussex, which organizes six-day walking tours of England, is offering all-expense jaunts through the Cotswalds, "Thomas Hardy's Dorset" and "James Herriot's Yorkshire" for about $370 per person, or a bit more than $60 a day (including all meals, lodging, guide).

Spain, Portugal, Greece and Ireland continue to be the best travel buys, say industry sources. France and Belgium -- where the quality of food and service traditionally are high -- are also top bargains. A three-course dinner in Belgium is about $7 on a "tourist menu." Even once notoriously expensive West Germany now has become much more affordable.

Italy, however, is no longer as inexpensive as it once was, although train travel is still phenomenally cheap compared with U.S. prices. One British tour operator has had to raise prices on trips to Italy, he says, because his hotel costs are up 13 percent, and restaurants on an average of 30 percent.

American shoppers in Europe, taking advantage of the strong dollar, have gone on a spree this winter as consumer goods seem to get cheaper by the day. If the exchange rate continues as favorable, plenty of bargains should remain this summer. Paul of American Express says the low prices on fine Italian-made shoes attracted her. On a recent business trip to Rome, she saw other Americans -- men as well as women -- buying as many as a dozen pairs.

Here is what the transatlantic traveler can expect this summer:

AIR FARES: Prices are up somewhat over last year, but not so much, apparently, that they are scaring off the customers. The range is so wide it will pay to do some comparison shopping.

Generally the best fares are for discount and charter flights, especially those originating from local airports. The scheduled carriers, however, offer more departures to more cities and full services.

Trans World Airlines, a scheduled carrier, is quoting a Washington-to-Rome round trip (via New York) of $849 (weekdays, 21-day advance purchase) during the peak season, June 1 to Sept. 14. This is up from $755 last year. TWA's Washington/Paris round trip (nonstop from Washington/Dulles) is $753, about $34 more than last year.

Pan Am is offering a round-trip fare from Washington/Dulles to London of $649 (weekdays, advance purchase) from June 1 to Sept. 14, an increase of about $100 over last year's peak fares. World Airways will have the same summer fare from Baltimore/Washington International. Until March 31, World is selling the cheapest Washington-to-London daily round trip at $338.

People Express, a discount airline, plans to offer a round-trip fare from Washington/Dulles to London (via Newark) for $398. From BWI and National (via Newark), the coach fare is $398 or $438 (depending on departure time). Virgin Atlantic Airways, another discounter, has announced $438 New York-to-London round trips from June 1 to Oct. 31.

Charter airlines, offering low-cost fares to the public, have mushroomed in recent years, providing strong competition to scheduled airlines. Travel Committee, a Baltimore-based charter operator, which schedules weekly flights from BWI between mid-May and October, has published round-trip rates beginning at $479 to London and $519 to Paris (cheaper if booked by March 15).

DER Charters, a West German firm, will fly Sundays throughout the summer from BWI to Frankfurt with a round-trip fare of $539 to $599. Council Charter of New York is advertising round trips from BWI to Amsterdam this summer at $444 and $484, depending on departure date.

Jet Vacations, a subsidiary of Air France, is offering New York-Paris charter round trips at $498 and to Nice at $538.

Travelers should be aware that charter flights operate under special regulations, and they have certain drawbacks. When flights are only once a week, for example, passengers who miss the plane run the risk of missing their entire vacation. TOURS:

Globus-Gateways says its prices are about the same as they were last year; American Express says on an average theirs "are generally lower" because of the strong dollar. Travelers can pick from no-frills budget weeks to super-deluxe itineraries of 30 days or more.

For first-timers abroad, TWA is scheduling the traditional "European Highlights" tour, seven countries in 15 days, for $649 to $728 per person (depending on departure date). The tour is a part of TWA's "Super Saver" program and includes lodging in "Super Saver" hotels, breakfasts, five dinners, touring and a gondola ride in Venice (air fare extra).

A similar itinerary in first-class hotels for 17 days ranges from $1,169 to $1,269 per person (air fare extra). TWA says it is now offering a cruise on 30 percent of its tours.

Cosmos Tourama, the budget end of the Globus-Gateway operation, has packaged a "European Mosaic" tour, eight countries in 16 days from $513 to $543 per person. Lodging is in tourist-class hotels, and the price includes continental breakfast, seven dinners and a ferry across the English Channel (air fare extra).

Jet Vacations has designed a first-class seven-day French Riviera tour at $510 per person (hotel, breakfasts, five lunches and two dinners; air fare extra).

In addition to guided sightseeing tours, Europe offers specialty and adventure tours for practically any interest, although they tend to be a bit more expensive: hiking, bicycling, gardens, music, art, archeology, mountain trekking, cruises, farm stays. Tours for teens, for under 35s, for senior citizens, for the physically handicapped. You name it.

One impact of the strong dollar is that tours are getting longer, say organizers. Americans can afford to linger in Europe a few extra days, and they are doing so. They want to take advantage of the favorable prices while they still can. CAR RENTALS:

Competition is stiff among car-rental agencies, so travelers this year should enjoy a "bonanza," says Henning H. Luessmann of interRent, an international car-rental firm.

His company, which takes bookings in the United States through Dollar Rent a Car or travel agents, guarantees prices at a set rate in the local currency. This means that as the dollar grows stronger, the weekly rental rate drops because a dollar buys more francs (or pounds or lire). On the other hand, should the dollar plunge, the cost of a car would go up.

At current exchange rates, many rentals are cheaper this year than they were last year, even though the price in the foreign currency is up. For example: Last year, interRent's cheapest car in France, a Renault 5, rented for 1,080 francs a week or about $130. This year, the rate climbed to 1,135 francs, but today that translates into about $115.

Rental prices range widely from country to country. Hertz, which also guarantees prices in local currencies, lists an approximate dollar rate for subcompacts at $118 weekly in Great Britain; $101 in Germany; $82 in Belgium and Luxembourg and $126 in France, based on advance reservations made in the United States.

Avis, however, guarantees its prices in dollars. The company argues that customers therefore know in advance exactly the price they will pay, since the dollar price won't fluctuate from day to day with the exchange rate. Avis' weekly subcompact rates are Holland, $94; Austria, $120; Ireland, $100; Italy, $98; Spain, $88; Portugal, $81; Sweden, $142.

Taxes should be taken into consideration, because they can increase the rental price dramatically. They are 5 percent in Spain, a bargain country for car rentals, up to 33.33 percent in France, one of the most expensive countries in which to rent a car.

Other current taxes: Austria, 21.2 percent; Belgium, 25; Denmark, 22; Germany, 14; Greece, 20; Holland, 19; Ireland, 18; Italy, 20; Sweden, 23.46; Switzerland, none; Great Britain, 15; and Yugoslavia, 15.

Overall, the best rates among the major gateway cities, says Luessmann, will be found in Amsterdam and Frankfurt. This is because in the two cities both the weekly rate and the taxes are moderate. In France, on the other hand, both are high. A traveler making a circle tour of Europe by auto, therefore, might find it cheaper to begin and end the trip in Amsterdam or Frankfurt rather than Paris. Says Luessmann: "When there is a choice of renting in either Germany or France, take Germany."

Some car rental firms also offer voucher programs for selected hotels. The traveler purchases a minimum of six vouchers per person for a choice of hotels throughout Europe at an established price, phoning ahead each day for that night's reservations. The vouchers offer travel flexibility matched with lower group hotel rates obtained by the rental agency.

Hertz, for example, offers vouchers in four price categories -- classic, traveler, adventurer and explorer -- to 3,200 European hotels. In Italy, the classic (the most expensive) is listed at about $49 per night per person. The explorer (the cheapest) is about $15 a night per person. MONEY:

How should travelers handle their money to take the best advantage of the fluctuating exchange rates? It's something of a gamble.

The difference in auto-rental pricing (local currency-guaranteed versus dollar-guaranteed) is an example.

If the dollar gets stronger, prices quoted in local currencies become cheaper for Americans. It takes fewer dollars to rent the car.

If the dollar weakens (and the local currency strengthens), it would take more dollars to rent the local-currency guaranteed car. The price of a dollar-guaranteed car would stay the same no matter how far the dollar plunged, a better buy in that situation.

Another example: When the Wayfarers of West Sussex set the price for the six-day English walking tours at 330 pounds a few months back, the dollar equivalent then was about $460. At a current exchange rate of 1.10 pounds to the dollar, the price has dropped almost $100 to $360.

If the traveler waits, and the dollar continues to strengthen, the price could get even cheaper. If the dollar weakens, the price could start climbing again, maybe even back to $460.

You make your decision based on which way you think the dollar will go.

One way to lock in current low car-rental and hotel rates -- if you think the dollar can go no higher -- is to prepay now. You won't benefit from any additional surge in the dollar; but you won't lose anything if the dollar drops.

While actually traveling abroad, if the dollar is in a strengthening trend, it might be wise to use a credit card for purchases. The exchange rate on the day the charge is processed (two weeks to a month after purchase) could be more favorable than on the day of the purchase, resulting in a savings.

For example, a Washington couple touring Italy last year saved more than $200 on hotel costs and purchases by paying with a credit card, because the dollar kept getting stronger daily. They gambled and won.

But if the dollar is weakening, avoid credit cards because the delay in processing could increase the price of any purchase.

A final big question is when to go.

If travelers have flexibility, air fares and tours generally are cheaper before June 1 and after mid-September.

But, perhaps as a result, May and especially September have become heavy travel months for Americans. Joseph of Globus-Gateway says the third week in September "is our busiest week of the year for departures." September is also interRent's busiest car rental month, says Luessmann.

Both American Express and Globus-Gateway say they experience a slight lull in transatlantic travel in August. That, however, is when many Europeans traditionally take their holidays.

Like the exchange rate, nothing is simple.