American Jet Industries Inc., a small, little-known aircraft refitting operation based at Van Nuys Airport, is poised to enter the big time, thanks mainly to the help of a financial angel from Las Vegas.

On July 18, the board of directors of Grumman Crop. announced that it had accepted in principle an offer from AJI of $52.5 million in stock and cash for Grumman American Corp, the Savannah, Ga., subsidiary of Grumman Corp. Grumman American had sales last year of $170 million. Its premier product is the Gulfstream II executive jet, which at a price of about $5.8 million is the most expensive private aircraft built today.

The deal still could collapse, but both sides optimistically are working out a final contract at meetings being held here and at Grumman's headquarters in Bethpage, L.I.

A complex variety of circumstances led to the proposed sale of Grumman American. Among the elements: rebellious stock-holders, allegations of payoffs to foreign officials, ongoing federal investigations that include a Washington grand jury, and a mysterious money man.

AJI, with sales of about $40 million last year, is the creation of Alan Paulson, 56, a former TWA pilot turned aviation entrepreneur. In his office decorated with models and watercolors of aircraft, the conservative Paulson is his own best example of the American capitalistic system that he fears is threatened by government interference.

Out on the airfield behind the office, AJI's mechanics refit a wide variety of jet and prop aircraft. One of AJI's specialities is installing cargo doors on the aircraft. The company sometimes buys used planes, then refits and sells them to foreign buyers.

AJI also does salvage work. For example, AJI bought the National Airlines 727 that crashed into Escambia Bay in Pensacola on May 8. The plane has been salvaged, and AJI is preparing it for resale.

But Paulson's pride is an innovative seven-passenger executive aircraft called the Hustler which cruises at 460 miles an hour, powered by a turnboprop engine up front and a fan jet in the rear.

The Hustler has gone through about 90 test flights and will be ready for customers who pay $760,000 in the fall of 1979, Paulson predicts.

To produce the Hustler in quantity, Paulson needed two key elements - a larger, more sophisticated manufacturing plant and the capital to finance.

In 1976, a Las Vegas venture capitalist and aircraft buff named Gerald Henderson saw an AJI advertisement describing the Hustler. Henderson apparently was intrigued by the Huslter's boast of "true twin engine safety" and the economies of turboprop.

Henderson, who is 73, not only ordered a Hustler's, he also bought 45 percent interest in AJI. The other 55 percent is held by Paulson.

His advanced years apparently did not deter Henderson from taking a flyer on a new business venture whose returns are years down the road. Henderson, like Paulson, is a loner, part of a vanishing breed of sole proprieters who do not have to justify their actions to stockholders or anyone else.

Henderson is recovering from an operation and was unavailable for an interview. However, Farrow Smith, the president of Henderson's company, Alexander Dawson Inc., furnished some background on his boss.

According to Smith, Henderson's interest in flying dates back to the late 1920s when he was a transport pilot. Smith says that only a year or so ago Henderson learned how to fly a helicopter.

The origins of Henderson's wealth were his investments years ago in Avon products, his pioneering of cable TV on the West Coast, and his ability to spot valuable land for development. Henderson's varied holdings include a crab meat canning operation in the Carolinas, a sheep and cattle ranch in New Zealand, real estate holdings in numerous states and a cardiovascular disease clinic in Colorado. In addition, Alexander Dawson has substantial precious metals holdings.

"We got out of the stock market two years ago," says Smith, who adds that Henderson held a New York Stock Exchange seat for a number of years in the 1960s.

The offices of Alexander Dawson are in the underground section of a building named after the firm. Henderson long has espoused underground housing. He exhibited a subterranean dwelling in the 1964 World's Fair in New York. Smith says that Henderson's 6,000-square-foot retreat in the Rockies is also underground.

Backed by Henderson's financial resources, Paulson began looking to expand his operation and to find a facility capable of producing his Hustler. AJI negotiated for about a year with Rockwell International to acquire that company's general aviation division, but negotiations broke down in June.

Soon after, Paulson got a call from a Grumman official who said his company's 80-percent-owned Grumman American Division might be for sale at the right price.

Grumman had acquired Cleveland-based American Aviation Corp. in 1973. Its owners, including the tough and demanding Art Modell, who also owns the Cleveland Browns professional football team, retained a 20 percent interest in the newly formed Grumman American Aviation Corp - They also got warrants they could exercise to increase their interest in Grumman American to 43 percent.

But from the start, Modell and two other Ohioans who are major former American Aviation shareholders, now minority shareholders in Grumman, attacked the policies of the parent Grumman Corp. They claimed Grumman Corp. was making self-serving decisions that were not in the best interest of all the stockholders. The trio has agreed to sell their shares in Grumman American to AJI and now the other 200 minority shareholders are being polled.

More recently the minority had been further troubled as Grumman's management has come under civil and criminal investigations. Both the Securities and Exchange Commission and the Justice Department are probing the company for alleged illegal payments overseas to promote sale of its F-14 fighter planes.

The cloud has extended over the Grumman American subsidiary, whose leading sales agent, Page Airways, has been accused by the SEC of paying off government officials in Africa and elsewhere to foster sales of the Gulfstream II. Page has denied the allegations.

The SEC investigation has further frustrated Modell and the other minority stockholders. The reason is that their warrants cannot be traded for stock until the transaction is registered with the SEC. But the SEC has blocked any registration because the agency claims Grumman American has not made full disclosure of its relationship with Page Airways.

With all this, it isn't surprising that Grumman is anxious to unload its troublesome subsidary. It also isn't surprising that the sale is favored by the minority stockholders, who could get their money, including the value of their warrants.

An SEC source said that the various investigations would continue even with the new management at Grumman American. Paulson, who says the new company would be renamed Gulfstream American Corp., says he is unconcerned about the SEC."I've never been involved in any of that," he says in his typically cryptic fashion.

If the deal is finalized, AJI will have to spend an estimated $40 million above the purchase price of the company to complete development of the Gulfstream III, an updated version of the current plane. Grumman will take part in building and marketing the plane, a Grumman spokesman said. Some of the necessary funds will come from Henderson. Paulson also says he has a line of credit from First National Bank of Chicago.

Grumman American has had problems with Gulfstream III, and some potential customers have abandoned their orders in favor of a Canadian version being developed by Canadair.

But Paulson is confident he can win them back. "They'll move back now," he predicts. And Smith says confidently:

"We're not too concerned about the Canadians."