When thinking of Canada, Americans probably envision a Canadian Mountie, with his trusty German shepherd, Rex, serenading dreamy-eyed damsels while tall pines whisper in the background.

What some Americans are only beginning to see is the chugging, heaving, sweating Canadian steel mills whose efficiency, profitability and low-cost steel may fast remove the romance from relations between the United States and its largest trading partner.

North America's fish, fur and lumber capital of the 1800s has become one of the most efficient steel producers in the world and the second largest steel exporter to the United States, behind Japan. Stelco, Canada's largest steelmaker, this year will open the world's first new integrated steel mill since 1974, while American mills are shutting down and laying off workers. The newest integrated (all manufacturing steps in one location) mill in America was built in the middle 1960s.

"The facility has all the latest techniques of production," said Donald F. Barnett, a vice president and economist at the American Iron and Steel Institute. "It incorporates all the cost savings and improvements we would like to have."

While some U.S. steelmakers, in the red, are crying the blues, Canadians are basking in the black. Stelco had profits last year of $156.9 million on $2.1 billion revenues, while U.S. Steel Corp., America's biggie, had a loss of $293 million on sales of $12.9 billion.

What is the price of success? U.S. Steel's Chairman David M. Roderick has hinted that he may file dumping or countervailing duty actions against the Canadian steel industry, a move that could result in heavy fines for the Canadians if they are found guilty. U.S. Steel would have to prove that the Canadians are selling steel here at prices below their costs of production or that the Canadian Steelmakers are receiving subsidies from their government to help them sell steel cheaply here and that those actions are injuring the U.S. industry.

But steel experts in Canada and here agree that it is unlikely the Canadians are violating any trade laws. They're just more efficient steelmakers.

The U.S. government several years ago even allowed some Canadian companies to sell steel here at prices below the trigger price mechanism -- a system in which steel imports brought into the country under a specific price automatically trigger a government investigation -- because they legally produce steel so cheaply.

One reason for the Canadians' success is "our tradition of expectations and momentum," said Henry C. Winters, general manager for marketing of Algoma Steel Corp. Ltd. of Sault Ste. Marie, Ont. "It's like being on the winning team," Winters paused, then chuckled, "like the Yankees."

But dumping really isn't a laughing matter, and the Canadians say they are watching U.S. Steel closely. The United States filed dumping complaints against the Canadians in 1977 involving pig iron, a minor matter that was never pursued beyond the complaint-filing stage, the Canadians said.

"We don't need to dump, Winters said. "And we don't want to dump. We want to establish long-term relationships with large companies in the U.S."

Winters also said his company is considering filing dumping complaints of its own against the Europeans and Japanese who are already targets of dumping actions by U.S. Steel. Both the International Trade Commission and the Commerce Department are investigation import practices of seven European countries in response to the U.S. Steel suit. U.S. Steel's Roderick said that Japan may be next and hinted that Canada had better watch out, too.

What has happened to a country that only 25 years ago imported about 30 percent of its steel and now has growing exports, particularly to the United States, envied profits and good morale among its workers?

Canadian steel executives and industry experts cite several reasons for their success such as cooperation between the government and industry, faster depreciation rates on equipment, continued modernization of facilities and emphasis on its own market rather than depending on exports. One of the problems of the U.S., European and Japanese steel industries is that Third World countries, to which they once sold steel by the boatloads, are producing it themselves and don't need foreign goods.

Besides producing only about one seventh of the amount of steel that the United States produces, the Canadians are "doing extremely well because of high domestic demand," Richard Heimlich, assistant U.S. trade representative, said of the Canadians. "They're reasonably modern and efficient with a couple of exceptions." Those exceptions are three old, small mills that have been salvaged by the Canadian government because they were located in regions with no other employment opportunities. The big three steel-makers, however, produce at least 85 percent of Canada's steel.

For example, Canadian steel is being produced at about 95 percent of the industry's capacity, compared with 60 percent capacity in the United States. Canadian steel imports have hovered around 2 million tons in the past five years while imports in the United States have dropped from 608,136 tons in 1975 to 517,489 in 1978, which are the most recent figures available from the Canadian government.

Steel exports to the United States, however, have grown from 650,000 in 1975 to 2 million in 1978, according to Canadian government figures.

Heimlich added that it is also difficult for foreign steel to enter Canada because shipping on the Great Lakes is closed during the North's long winter season.

Demand for steel is relatively high in Canada because the government and industry are pushing public works and construction projects in the large unused Canadian expanse that is being developed, the AISI's Barnett said.

"The Canadian economy is at a stage to use more steel" such as in pipelines, rails and roads, Barnett said. The Canadian steel market is growing by 4 percent to 5 percent a year while the U.S. demand is increasing by slightly more than one percent, he added.

Another explanation is that Canadian companies have good cash flow caused by a rapid depreciation schedule for equipment that permits them to reinvest more money quickly into more machinery. In Canada, manufacturers can depreciate equipment after two years whereas in the United States they must wait 12 years for full depreciation, Barnett said.

"That makes a great difference in cash flow. They're more effective in fighting inflation because of depreciation," Barnet said. So there's incentive to keep investing because you get your money right back."

American business people have long lobbied for faster depreciation and several bills addressing that problem have been introduced and are pending in Congress. The bills have numerous sponsors, however, many of those sponsors, are having second thoughts about such legislation because it could cost the government billions of dollars at a time when balancing the budget is important.

Although U.S. steelmakers invest much of their profits in non-steel endeavors, the Canadians pour almost all of theirs back into equipment. Some U.S. steelmakers said they invested in the nonsteel businesses to shore up the steel divisions and keep their corporations afloat. Executives at Algoma and Dofasco said their subsidiaries are mostly steel-related and aren't necessary to carry their businesses. Representatives of Stelco declined to be interviewed.

At the same time the Canadians are able to boost workers' morale by offering generous bonus plans. For example, at Dofasco 11 percent of the company's profit is given to the workers in across-the-board bonuses, Goddard said. Dofasco has no union.

The other steel works, however, have workers covered by the United Steelworkers of America. But their contracts aren't as rich as those of their American brothers, partly because the value of the Canadian dollar gives them a discount, Barnett said. There have also been wage and price controls in Canada from time to time, "seemingly at times when wage contracts come up," Barnett added. U.S. steelworkers' wage rates are higher than those of the average American factory worker while Canadian steelworkers' wages are about average for manufacturing industries, Barnett said.

Despite their good fortune, Canadians, too, battle the government with regulations, environmental costs and other skirmishes fought by their American counterparts, Bartlett said. And, since their profits are higher, they also pay more taxes.

In addition, Canadian steel executives said they are experiencing a severe drop in demand, although, unlike the Americans, they don't expect it to last very long and look forward to a profitable year anyway.