America's "Big Three" car companies became America's "Only Three" car companies yesterday."

American Motors Corp., the only other purely domestic auto maker, became part of Chrysler Corp. in an overwhelming vote by AMC stockholders approving a nearly $2 billion takeover of their company. The transaction leaves General Motors Corp., Ford Motor Co. and Chrysler as the only native American auto manufacturers.

Some might view AMC's long-expected demise as proof that the U.S. auto industry is shrinking. That is incorrect. There are more companies manufacturing and selling cars and light trucks in the United States today than there were 20 years ago.

And by 1990, there will be more auto makers in the country than there were in 1954, when AMC was formed as the result of a merger between two failing car companies, Nash-Kelvinator Corp. and Hudson Motor Car Co.

The difference is that most of the new companies building vehicles here will be foreign-owned, or they will be joint-venture operations involving U.S. and foreign companies. Among them will be Honda Motor Co. Ltd., Toyota Motor Corp., Volkswagen, Mazda Motor Corp., Nissan Motor Co. Ltd. and Mitsubishi Motors Corp. Many auto industry analysts are predicting that South Korean auto maker Hyundai Motor Co. Ltd. will set up shop on U.S. soil too.

Figures vary, but a consensus among those watching the U.S. auto market is that foreign car companies building in America -- so-called "transplants" -- will be able to produce 1.5 million cars annually for U.S.-market sales by 1990.

Light trucks are another matter. The category includes pickups, vans and sports utility vehicles such as the Jeep Cherokee and Isuzu Trooper. Foreign-owned production of light trucks in the United States could push total transplant-vehicle manufacturing over the 2 million mark in the early 1990s, according to figures presented by auto industry experts at the 12th annual Automotive News World Congress meeting in Detroit last month.

Transplant production combined with import sales are giving foreign auto makers a bigger share of the U.S. market, thus putting tremendous pressure on the three native auto makers. For example, in the matter of car sales alone, Japanese imports account for 22 percent of the U.S. market, European imports take 6.6 percent and imports from Yugoslavia and South Korea have another 3 percent, according to figures for the first five months of 1987 compiled by Merrill Lynch Economics Inc.

Transplant production boosts the foreign share to more than 30 percent of the U.S. auto market, according to Merrill Lynch & Co.

Those numbers might bring hunched shoulders in a market that last year sold a record 16.3 million cars and trucks, and that is expected to sell a still-healthy 15 million vehicles in 1987. But too many cars from too many manufacturers bode ill for everybody competing in the U.S. auto market, analysts say.

"The biggest fear in the U.S. auto market is excess capacity," said Maryann N. Keller, an analyst with Furman, Selz, Mager, Dietz and Birney Inc. in New York. Some auto industry officials, such as Ford President Harold A. Poling, believe that "excess capacity" will amount to 7 million cars and trucks a year in the North American market, primarily the United States, in the early 1990s.

That means "domestic as well as European auto makers will be struggling to hold onto market share," Keller said. On that battlefield, there is virtually no room for an AMC, a company with limited product offerings that held less than one percent of the U.S. market, according to Keller and other analysts.

AMC officials, many of whom are moving to positions in Chrysler, grudgingly agreed with the analysts yesterday at a merger ceremony in Highland Park, Mich.

"I want to disabuse anyone of the notion that this merger is the case of a failing company falling prey to a more successful competitor," said Joseph E. Cappy, AMC president and chief executive officer. "AMC is not a failing company," said Cappy, who will become a Chrysler group vice president in charge of marketing AMC's famed Jeep vehicles.

The problem was that AMC could not "stay the distance in the face of burgeoning competition out there," Cappy said.