The Soviet missile inspectors in Utah may be catching the headlines this summer, but the real invasion is apparently from Germany.

Record numbers of foreign tourists are visiting Utah this year, and Germans are leading the pack. They are attending Days of '47 events in hordes this week.In fact, it has been so crowded on Temple Square that one guide commented, "It's like Christmas lighting week." More than 170 all-German bus tours have already visited the square this year.

The West Germans, who outnumbered the French and Japanese tourists visiting Natural Bridges National Monument last month, credit a highly favorable exchange rate (currently their buying power is nearly double in this country), low air fares and a Utah promotional film with enticing them to spend their vacations in Utah.

Titled "Wo der Regenbogen Schlaft" (Where the Rainbow Sleeps), the German narrated film was first broadcast in Germany in January and rebroadcast there and in Switzerland and Austria over the past several months. About 25 million Germans saw the film on New Year's Eve alone.

Utahns who have reaped the proceeds in tourist trade can thank Bob Jones, owner of Tag-a-long Expeditions in Moab. In the course of his marketing campaigns, Jones was contacted by the U.S. Department of Commerce's Division of Travel and Tourism Administration. A native German on staff, who had been on one of Jones' river trips, recommended that a film of Utah be done to help promote the United States abroad.

Financed by the federal government, in cooperation with a Germany television station, the film - which highlights many of Utah's spectacular sites - was produced by Dr. Otto Guggenbichler, a director of Channel 1 in Germany, and sold to other German television stations.

"It's incredible that this state, which is such a sleeper in many ways, was selected to promote European travel to the U.S.," Jones said. "They put all of their dollars into Utah, and it didn't cost the state anything." In fact, some of the people who participated got paid.

"It is just because of how strongly and well the people in Europe think of this area," Jones said. "It makes me laugh that when I am in Paris or Munich, Moab gets more recognition than in some places in Utah. Southern Utah has a tremendous recognition in Europe."

The film was in part responsible for the state's foreign fame.

"It was done very nicely. It brought nature into the living room," said Karin Blanke, who was visiting the state with her husband George. "We definitely said we have to see it (Utah). We called my sister and said we have to go."

George Blanke's sister-in-law, Barbra Landschreiber, joined the couple on the trip to Utah, and said they would not have toured Utah if they had not seen the film.

"I thought everything was in Colorado and New Mexico," she said. "If you would do movies like that - the United States is such a big country, Germany is 800 miles across and we cannot imagine such a country as the U.S. - we would like to watch movies like that . . . and people would know where to go."

Paul Guraedy, superintendent of Arches National Park, has also heard the Germans praise Utah.

"One group (of Germans) said they like other phenomenons like Disneyland and New York, but where can they go to see anything like this? Our parks are completely different from anything they've seen," he said. "The same thing can be said of the Japanese, the second largest group of foreign tourists visiting the park."

According to Guraedy, the German influx to Utah parks isn't unique to 1988. "It rises and falls with the relationship with the dollar and deutsch mark," he said.

This year it's on the rise. Of the 90,000 visitors to Natural Bridges National Monument this year, a third are foreigners; the largest percent of those are German.

Dick Elzinga, German rental agent for Cruise America-RV Rental in Murray, said about 70 percent of their business this summer has been to German-speaking people. "Because the dollar is so low, all of the people who couldn't afford to see America before are seeing it now."

The regional sales manager for Lufthansa German Airlines said vacationers from Germany are increasingly including Utah in their travel schedules.

"More German people are coming to the United States this year than ever before, and it seems they all want to come to Utah" Walter R. Maschmeyer said during a recent visit. "I don't understand this."

Part of the explanation could be that they want to visit Temple Square, according to Quig Nielsen, public relations director for Temple Square.

Nielsen said overall bus-tour numbers have reached an all-time high.

"The number of motor-coach tours scheduled for the square this year is 953, compared with 891 during all of 1987," Nielsen said, "and summer's just starting."

"Our tour manager, Margaret Farnsworth, reports that already more than 500 of those 953 scheduled motor-coach tours have visited the square, with Germany's 100 thus far leading the way, Chinese groups second and Japanese tours third," Nielsen said.