BETTE DAVIS, Peter Ustinov, Angela Lansbury, Mia Farrow, David Niven and a host of their fellow thespians have become unofficial public relations agents for the Egyptian tourist industry.

Two years ago they were in "Death on the Nile," a multi-star Agatha Christie thriller which unfolded aboard a steamer cruising the mighty, muddy river. Besides offering suspense, the picture provided dramatic views of Egypt's scenic wonders and made crusing the Nile look like the way to find romance and the thrill of exploring an alien land.

With the movie's success came a boom in the tour business, as fleets of vessels -- from said-powered feluccas to diesel-powered ships -- reported more demands for space.

"'Death on the Nile' was good propaganda for Egypt, especially for Nile cruises," chuckled Tawfik Kamal, who has heard many visitors cite the film as their reason for coming to the land of the Pharoahs. Kamal is the manager of the Tut, a $10-milllion vessel that is one of four Nile boats operated by the Sheraton hotel chain. The Hilton hotel organization runs two.

Although visitors may come to Egypt hoping for a contemporary version of "Death on the Nile," the luxury they find on a ship like the Tut may remind them more of "The Love Boat." Like the other Nile cruise ships, the Tut offers excursions between Aswan and Luxor, and its layout is typical of this breed: Besides 87 air-conditioned cabins on four decks, it has a spacious dining room, an ample sundeck carpeted with artificial turf, a swimming pool and a bar with a mini-disco that has a brass dance floor, flashing lights and a powerful sound system.

Guests who want more soothing music can simply push a button on the multi-channel speaker in each 8-by-12-foot cabin and get an earful of "elevator music" -- sugary instrumental renditions of "I Could Write a Book," "Honey," "Desire" and "Here You Come Again," and over and over and over.

Generally, Nile cruises are included in package tours, but they can be booked separately. Rates are higher during the so-called winter season (Oct. 1-May 21), when the outdoor temperature is somewhat lower than that of a brick kiln. During that period a single cabin is $657, and a double cabin is $829 (that is, $414.50 per person). In th summer months (June 1-Sept. 30), a single cabin costs $557,and the double-cabin rate is $643 ($321.50 apiece).

All prices include meals, shore tours and tips.

"Everyone likes the luxury," said Anna Sterk, a tour guide from Delft. "Everyone likes the air-conditioning after all the heat outside."

However, Sterk, who has led several groups on Nile tours, said the frequent exposure to tempeature extremes -- intense outdoor heat and intense indoor air-conditioning -- touches off more bouts of illness than the food.

At one point on our cruise, about 50 of the slightly more than 100 passengers were ill. When Sterk heard that, she explained that the frequent changes in temperature constitute the coup de grace for body systems that already may have been upset by changes in climate, daily routines or cuisine.

However, the food on these trips shouldn't upset any but the most delicate constitutions. Served in elaborately laid buffets three times per day (two seatings per meal), or fare was primarily American, with a few Middle Eastern dishes such as moussaka, humomus, fatta, felafel and cooked barley thrown in for the more adventurous.

The breakfasts were as American as the food at any U.S. diner, with bacon, eggs, juices and several types of rolls. At lunches and dinners, salads were dominant -- a blessing on hot days -- along with four or five hot entrees.

The food was well prepared and, in many cases, well decorated. To call attention to the fact that we were abroad a Sheraton ship, a cold salmon mold was served in the shape of a big S, and whole fish frequently were surrounded by a colorful forest of greenery.

Desserts -- tarts, custards, sinfullyrich cakes and pastries -- were tempting and abundant. If there was any danger from these meals, it wasn't from the type of food eaten but from the amount. Overindulgence was a problem for all but the most fastidious. In the dining room, bar service was available (drinks extra). Stella beer, served ice cold, proved an excellent way to forget the heat, and big bottles of mineral water were on sale.

Besides "Death on the Nile," the Camp David accord between Israel and Egypt brought tourists into this region -- and onto these ships -- before relations between the two countries began to cool. In Aswan, Alisa Begin and Jihan Sadat had boarded the Tut for lunch while their husbands were still participating in peace discussions. Kamal displayed a wad of color photographs of the occasion, and his guests' signatures -- including a message in Arabic from Mrs. Sadat -- are in the Tut's guest book, along with praises in several other languages from satisfied guests.

Among the influx of cruisers are Jewish guests. On my Tut cruise was a delegation from the United Jewish Congress, and when I remarked to Stella Epner, a member of that group, that she probably couldn't have pictured herself on the Nile 10 years ago, she huffed, "Ten years ago? Two years ago I couldn't have pictured myself here!"

"Tourists make the Nile cruise for one reason: It is the easiest way to see Upper Egypt," said Kamal, referring to the region of southern Egypt called Upper Egypt because it is upstream from nothern Egypt. "Instead of going to Luxor and sightseeing and then taking a plane to Aswan, this is much easier."

And Aboard these ships, the emphasis is on ease. Passage includes temple tours, but these are optional, and between stops passengers can gorge and also take tea -- tea, coffee, sandwiches and cakes -- in the bar at 5 every afternoon. Serving the guests -- capacity is 198 -- are 115 crew members, including kitchen workers who are also skilled Nubian dancers.

"God, I wonder what the poor people are doing today," said Sheri Galper as she rubbed suntan lotion onto her body, sank into a chair on the Tut's deck and closed her eyes in the harsh sunlight. Any passenger who looked would have seen scores of poor people -- families along the banks who live in shacks while tilling the Nile-Enriched land -- but to those of us aboard the Tut such reality seemed far away.

Reality intrudes only when tour leaders remind travelerse that Nile water is for seeing, not drinking, and that the use of bottled water is advisable.

The distance between Aswan and Luxor is only 140 miles, and all the traveling is done in less than two days at a top speed of about 30 miles per hour. However, the Tut's cruise time is stretched to five days because of sight-seeing expeditions at each end of the line which take most of two days apiece. En route, there are stops at several temples.

The first stop out of Aswan, the temple of Kom Ombo, was "a quickie temple," said Herb Galper, who dashed back to his cool quarters on the Tut after 90 minutes among the ruins. Those who lingered saw a primitive example of a speaker system that the temple's priests used. Whenever a ruler addressed questions to the gods, a priest stood in a tunnel beneath the floor to provide responses. The tunnel network, which had openings in walls on opposite sides of the room, amplified his voice and made his answers impressive.

Nearby were mummies of crocodiles, neatly preserved and stacked -- after all, this was a temple built to honor Sobek, the crocodile god -- and on the way back to the boat we saw a turbaned man squatting in the sand who reached into a straw basket and pulled out a cobra. He said it wasn't poisonous anymore, and posed with the snake for pictures in return for "baksheesh" -- small change.

Kom Ombo was within a few dunes of the boat landing, but at Edfu, the next stop down the Nile, we boarded hantours -- canopied horse-drawn carriages -- for the ride throught dusty streets to the temple dedicated to Horus, the sun god.

The carriages made us feel like "Death on the Nile" characters, and we probably looked awfully affluent to the natives -- expecially the children, who chased our hantours asking for handouts. In response, one vigilant tourist policeman, anxious to insure that we were not harassed or ripped off, hit one child and sent him sprawling in the dust.

The temple took 200 years to build, and the horses that brought us there must have thought we were taking that long to tour it. My hantour's horse showed his frustration by taking a big bite out of the neck of a driver standing in front of him. The man screamed, and his colleagues beat the horse until he let go.

After we had been taken back to the boat, most of us repaired to the sun deck to improve our tans, read -- cheap mysteries, gothics, love novels and books about Egypt dominate -- or to stare at the landscape, which consisted of fertile soil near the river, desert just beyond the greensward and, far in the distance, mountains.

In the farming areas, children and their parents gathered along the riverbanks to wave at us. When Dolores Luber of Montreal spotted some naked children who waved at us and wiggled, she said with a touch of wonder, "Oh, is that some sort of ritual?" Replied Lee Crum, a blunt New Orleans photographer: "It's sex."

The polyglot group -- tourists from the United States, France and the Netherlands -- would congregate after tea on the sundeck each day to see the brilliant sunset before proceeding downstairs for dinner.

By night, most passengers headed for the bar. On our next-to-last night out, we had a costume party where Sheri Galper won the best-dressed prize by wrapping herself in toilet paper and brandishing a sign reading, "Hands Off My Tuts."

The Nubian dancers on the kitchen staff performed a ritual that night that was supposed to celebrate a harvest, and they pulled partygoers out of their chairs to form several circles of chanting dancers on the brass floor. Said Dolores Luber: "At a Jewish wedding this would become a hora." On our last night out there was another party, where the featured entertainment was a nimble belly dancer.

Out on the Nile, far away from big cities like Cairo and Alexandria, it was almost possible to forget that such metropolises existed, and passengers who weren't sunning, swimming, napping or reading could enjoy sights that hadn't changed for thousands of years: water buffalo wading, several herds of sheep and goats and piles of neatly arranged urns, newly made and put outside to dry.

After such classic vistas, many cruisers howled with dismay as we pulled into Luxor past neat rows of red-orange --, and white-striped house trailers neatly arranged on the bank like tract houses.

In Luxor, as we stood outside the sprawling temple of Karnak with the temperature over 100 degrees, one woman clutched her bottle of water wrapped in a wet washcloth and said, "I think today would be a good day to faint."