Add another to the long list of American industries that have been hit hard by declining demand and increased foreign competition: automobiles, steel, shoes, textiles, shipbuilding, and now, eggs.

Eggs are still big business -- some 279 million chickens are turning out 68 billion eggs a year -- but there's trouble in the henhouses. The number of working egg farms has declined from about 6,200 to fewer than 4,700 since 1980, according to the producers, and exports have dropped by more than 50 percent in the past year.

With prices falling in a glutted market, American producers are blaming foreign competitors. Egg farms owned by Japanese and German corporations are expanding their capacity despite the oversupply, and European nations are illegally subsidizing egg exports to take over markets formerly held by Americans, the egg producers say.

According to Floyd Lasley, director of poultry research at the Department of Agriculture, the egg producers' problems predate the growth of foreign competition, but have been aggravated by the aggressive policies of overseas corporations entering the U.S. market.

He said per capita consumption of eggs is dropping for many reasons, ranging from concerns about cholesterol to a decline in home baking, but production has stayed high because mechanized egg farms are capable of turning out more and more eggs with less and less labor. "When you have those new facilities, your costs aren't less even if you cut back production," he said, "and if you borrowed to pay for it you have to sell eggs to meet your fixed commitments."

The producers estimate that 15 percent of all the laying hens in this country are now owned by foreigners, and foreign investors continue to increase their capacity despite the oversupply, apparently anticipating long-term dominance in a shrunken market.

Gene Newsom, president of Landmark Inc., a large producer cooperative in Columbus, Ohio, said Japanese and German companies now own 38 percent of the 10 million laying hens in that state. He said one of the largest farms, Croton Egg Farms, where the land and buildings are owned by a German and the birds are owned by Americans, was planning to expand from 2.5 million to 5 million hens, further saturating the glutted Ohio-Indiana market.

Dick McGrath, Croton's American operator, said the farm is owned by Anton Pohlmann, whom he described as the biggest and most successful egg farmer in Europe. He said Pohlmann "has money to invest, and he wanted to invest it in the business he knows best, in the land of the free and the home of the brave, where there's a stable government."

But, McGrath said, Croton may hold off on expansion because of depressed prices. He said he graded a site for expansion because he expected the New York quoted price to hit 82 cents per dozen by December, but it has hovered at about 71 cents.

Pohlmann has reportedly invested $33 million in the Ohio facility, which McGrath said was able to produce chickens at low cost because of its modern equipment and its proximity to corn supplies.

Because of fears about the output of such modern, foreign-financed farms, Midwest Egg Producers, a cooperative based in Eldridge, Iowa, declared in a recent newsletter that "foreign investment in the laying hen business is unfair competition. It has resulted in unwarranted expansion at a time when we did not need it for domestic use. It has contributed to a severe undermining of profitability in the egg business, and has cost U.S. egg producers millions of dollars."

United Egg Producers, a Decatur, Ga., federation of egg-farm cooperatives whose members account for about 60 percent of U.S. production, adopted a resolution declaring that "entry by foreign investors into the U.S. egg production agriculture will will be greeted by U.S. egg producers as entry into a hostile environment."

The resolution called on the federal goverment to discourage further inflows of foreign capital into the business, but the Reagan administration has repeatedly proclaimed a policy of supporting foreign investment as beneficial to the overall U.S. economy.

The problems caused by the expansion of foreign-owned capacity in this country have been compounded by a sudden collapse of the export market. According to Agriculture Department statistics, the U.S. exported 68.3 million dozen shell eggs for eating and cooking use in the first nine months of 1981 and 34 million, or less than half, in the same period of 1982.

Lasley, the department's poultry specialist, said that "on a percentage basis, the export market was rather small, but if you back up that lost export into our domestic market already high on the supply side, you get a tremendous magnified effect."

According to Albert Pope, president of United Egg Producers, the main reason for the drop in exports is that France and the Netherlands are subsidizing their egg producers, enabling them to undersell their American competition in key markets such as the Middle East.

The issue of European agricultural export subsidies is a longstanding irritant in trade relations between the United States and Europe -- producers of sugar, flour, broiling chickens, pasta and other commodities have lodged similar complaints -- but the egg producers have refrained from filing a formal complaint with the office of the Special Trade Representative.

"You need at least $50,000 for the legal work," Pope said, "and some of these cases stay around for years with no indication that there's going to be any result."