Will hordes of American travelers again swarm the streets of Europe this summer?

The transatlantic tourist industry certainly hopes so and is cautiously optimistic, although several large tour operators report that bookings for the summer are down so far this year.

Last year, an estimated 6.5 million Americans visited Europe, a banner year by most accounts -- and "a hard act to follow," said Bruce Haxthausen, a spokesman for Air France in New York, one tour operator that says its bookings actually are showing an increase.

This year, however, the travel industry is facing two major problems, both of which have a potential to reduce the number of Americans abroad: the declining dollar and the threat of terrorism. Of the two, fear for personal safety seems to be worrying travelers the most.

Nevertheless, the French airline's advance reservations through June 30 are up six percent over last year at this period, Haxthausen said, and some flights from New York to Paris in June, when schools let out, already are almost filled. "Based on these numbers, we are optimistic, but we aren't taking anything for granted."

Other tour operators, however, said they will be happy if they manage to send at least as many Americans to Europe as they did last year.

To reach even that goal in the present sk,2 sw,-2 ld,10 atmosphere, they expect to have to hustle harder to sign up travelers. A year ago, the travel industry was experiencing what Jay Rising, director for European travel for American Express, called "a booking frenzy" for summer travel to Europe; this year, he said, the market "is softer" and bookings are coming more slowly.

Globus-Gateway/Cosmos Tourama, another major packager of tours to Europe, is also reporting a slow start in bookings, especially from individual travelers. To accommodate people who do sign up, said managing director John Martinen, the company will, if necessary, schedule trips with fewer tourists than the minimum required last year.

Despite the emotional fallout following the terrorist attack on the Rome airport on Dec. 27, Perillo Tours of Pearl River, N.Y., which specializes in trips to Italy, anticipates taking about the same number of Americans to Italy this year as it did last year -- about 40,000, according to spokeswoman Margaret Toupin.

Among some tour operators, there is a feeling that they will see fewer first-time travelers to Europe, but they anticipate that Americans who have been there already will not be deterred -- so long as no new terrorist incidents erupt. "The repeat traveler is not as concerned by these unfortunate incidents," said American Express' Rising.

Martinen of Globus-Gateway said his firm is seeing its heaviest demand from small groups of travelers. "Maybe people feel more comfortable in groups from their home town."

Meanwhile, some popular vacation destinations in the United States, including Walt Disney World in Orlando, Fla., are reporting heavier than usual early bookings for this summer, suggesting that more American travelers will be spending their holiday on this side of the Atlantic.

"There's no doubt whatsoever we have been affected by the pictures of the bodies on TV," said Donald Ford, general manager of the British Tourist Authority in New York, referring to the terrorist attacks Dec. 27 on airports in Rome and Vienna.

Perhaps the biggest drop-off, Ford said, has been in student tours from the United States. School administrators are leery of sending youngsters where there is any question about their welfare. Ford has been visiting U.S. cities with other European tourism officials trying to reassure the traveling public.

According to a poll commissioned by Travel Weekly, a travel industry publication, almost half the nation's 26,000 travel agents had one or more clients who changed or canceled their plans because of two earlier attacks on travelers. These incidents were the hijacking of TWA Flight 847 in Athens last summer and the seizure of the Italian cruise ship Achille Lauro in the Mediterranean last October.

The European Travel Commission, a travel promotion organization that represents the tourist offices of 23 West European countries, is trying to convince American travelers they "are as safe in Europe as they are at home."

In keeping with the positive image it wants to project, the commission has issued a statement asserting that "security at European airports and seaports . . . is steadily being improved, and tighter controls of passenger and baggage movements are being implemented." The problem with the declining dollar, according to travel industry spokesmen, is one of perception. The dollar is dropping, but travel to Europe remains a good buy.

In 1983, 1984 and 1985, travelers could read almost daily stories about the surging strength of the dollar in Europe and the resulting bargains in hotels, meals and shopping. There was a sense of urgency to take advantage of a good deal while it was still possible.

For the past half year or so, the stories have been about the dollar's steady decline -- and that decline has been substantial. Otto Reusch of Reusch International Monetary Services of Washington estimates the dollar has dropped 20 to 40 percent against the major European currencies in the past year.

But, as Ford of the British Tourist Authority pointed out, the dollar is still much stronger than it was before it began its big climb. In February of last year, when the dollar reached the height of its climb, the exchange rate was one British pound to $1.05. Now a pound costs about $1.45. Five years ago, however, a pound cost about $2.20.

London, though not the bonanza it was a year ago, "is still a good value for shopping," said Ford. The best theater tickets in town are about $20 to $25, considerably less than the $45 or more now charged in New York City.

One non-European country where the dollar has actually been getting stronger is Canada, which has great expectations for a big travel year because of the 1986 World Exposition that starts May 2 in Vancouver, British Columbia, and runs to Oct. 13. It is expected to attract 15 million visitors, a great many of them from the United States.

At current exchange rates, a Canadian dollar costs about 75 U.S. cents. Americans should find it "an unbelievable value," said Laverne Barnes of Tourism British Columbia, the province's tourist office.

The bill for a deluxe dinner for two in one of Vancouver's finest restaurants might come to 100 Canadian dollars, she pointed out. But in U.S. currency, that's about $75 -- not a bad price for the best meal (with wine) in a quite sophisticated dining town.

While the dollar has declined in many popular European destinations -- Great Britain, the Netherlands, Germany, Switzerland and France -- travelers to Europe will continue to find the dollar an especially good value in Spain, Portugal and Greece, according to Reusch of Reusch International Monetary Services.

In fact, in Greece the dollar was buying slightly more in February of this year than it did in February of 1985. "Greece is a bargain for shopping," said George Kouros, director of the Greek National Tourist Organization in New York.

However, as a result of the Athens airport hijacking, Greece is facing an uphill battle to attract the estimated 485,000 Americans who visited the country in 1985. To try and convince travelers that the country is a safe destination, the tourist office has just launched a special, two-pronged publicity campaign.

Before spring is over, said Kouros, about 2,000 U.S. travel agents will be flown to Greece for a "familiarization tour"; the hope is that they will report back favorably on vacation possibilities to their clients.

And 37 actors and sports celebrities, among them E.G. Marshall, Polly Bergen and Joe Namath, have been enlisted to promote Greece in a series of 30-second television commercials in several U.S. cities. In exchange, they get a week's trip to Greece. In other developments on the European travel scene:

*American Express is reporting a heavy demand for trips to the Soviet Union and other Eastern European countries. Jay Rising sees it as a sign of repeat European travelers who have visited Western Europe and are moving on to new destinations. At the same time, Eastern Europe is a good travel buy, he said.

*Air France is focusing on the repeat traveler by offering a new series of unescorted package tours called "Paris Plus." The idea is to attract travelers back to Paris for two to four nights before they fly off to some other country.

According to Air France, travelers who book a Paris Plus tour get a room in a quality Paris hotel "free."

For example, the airline is selling a 13-day tour to Vienna (five days); Budapest (five days) and Prague (three days) for $779 per person, which includes lodging, most meals and sightseeing tours (air fare is extra). The price also includes the two "free" nights in Paris, a boat cruise on the Seine and airport transfers.

*Great Britain is anticipating a good year, and tourism officials would like to attract at least 3.3 million Americans, the same number as last year -- a record for travelers from the United States. "We'd be more than happy if we hit the same number," said Ford.

He bases his optimism on the success of the "Treasure Houses of Britain" exhibition at the National Gallery, which has been extended through April 13. He hopes the show will interest art lovers in visiting some of the actual treasure houses in Great Britain.

Along with the exhibit, the special British Travel Centre at the Old Post Office Pavilion on Pennsylvania Avenue NW also will remain open through April 13. The tourist office provides information and brochures about visits to Great Britain and its historic homes. Operating hours are 10 a.m. to 6 p.m., Monday through Saturday.

*Trek America/Trek Europa of Staten Island, N.Y., which organizes small-group camping tours of Europe for the 18-to-35 age group, claims its European business is mushrooming. "Our bookings are very, very strong," said spokesman Mark Sheehan.

Part of the firm's appeal, he said, is "we travel incognito," by which he means that a van with no more than 14 young passengers does not attract much attention.

One of the firm's biggest sellers is its four-week "Red Star" drive through the Soviet Union, Czechoslovakia and East Germany. The cost is $1,189 to $1,289 per person (depending on departure date) for most land costs (air fare extra).

What all this means for Europe-bound travelers is that they can still enjoy a vacation that is something of a bargain -- though not quite the great buy it was for a while.

And they probably don't have to rush immediately to make reservations for flights, tours, hotels and restaurants. The transatlantic travel industry made room for 6.5 million Americans last year, and it has that much -- or more -- space available this year.

Most tour operators contacted said it was too early to tell if European hotels would drop their prices if the hordes of Americans don't show up this year. However, American Express said it has begun renegotiating lower rates for some hotels on its tours.

Air fares are not expected to increase by much if any this summer because of increasing competition on transatlantic routes among scheduled, discount and charter airlines.

When the dollar is declining, travelers should remember to alter their currency exchange strategies:

*Consider buying foreign currency or traveler's checks in foreign currency now to lock in the present rate of exchange, if you think the dollar is going to continue dropping. This decision is something of a gamble, but an educated one if you keep up to date on news reports of the dollar's activity.

*Pay now for as much of the trip as you can, again to lock in current exchange rates if you think the dollar is on a downward trend.

*Be cautious about charging large purchases on a credit card while you are abroad. The exchange rate on the day the charge is processed -- one or more days later -- may not be as good as the rate on the day you used the card. You might end up paying more than you expected.