Tens of thousands of air travelers stranded in Europe and the United States began flying across the North Atlantic yesterday after Canadian air controllers ended their two-day boycott of flights to and from the United States and reopened the main aviation corridor across the ocean.

Although flight delays continued, airlines reported they had restored most flights canceled Monday and Tuesday in response to the Canadian controllers' action. Transatlantic and Canadian-U.S. traffic was expected to return to near-normal today.

Early yesterday the Canadian government and the Canadian Air Traffic Controllers Association announced an agreement to end the job action, which the union said it called to protest U.S. emergency flight control measures taken in the wake of a walkout by 13,000 American controllers on Aug. 3. The Canadian union alleges that U.S. airspace is unsafe under the emergency measures.

The agreement announced yesterday ended -- at least temporarily-- the most disruptive reaction thus far to the strike by U.S. controllers, 12,000 of whom have been fired by the Reagan administration.

Robert E. Poli, head of the U.S. controllers' union, chartered a bus yesterday to go to New York to give a deposition in federal court concerning fines of $4.5 million levied against his union. Poli said he went by bus because U.S. airspace is unsafe.

The Canadian controllers agreed to resume normal operations in exchange for creation of a dozen fact-finding teams, with government and union representatives, to investigate alleged safety violations in cross-border air traffic. The initial results of their studies could be released this weekend, union president William Robertson said yesterday.

The two-day near-paralysis of transatlantic flights was caused primarily by the closing of the control center at Gander, Newfoundland, where about 100 controllers guide aircraft halfway across the Atlantic along the "Great Circle" route, the most direct and heavily traveled.

Yesterday morning, with controllers at Gander again accepting U.S. traffic, airlines moved quickly to clear a backlog of irate passengers stranded by the action. "Canceled" signs came off airport flight schedule boards and passengers crowded aboard wide-bodied jets for the trip across the ocean.

Federal Aviation Administration head Lynn Helms said that between 6:30 and noon yesterday, 119 flights, or about 20 an hour, arrived from Europe, carrying about 36,000 passengers. Only five planes per hour moved along alternate routes established Monday and Tuesday to skirt Canadian-controlled airspace.

Helms said 70 more planes and 21,000 passengers were expected to arrive from Europe by early last night. Flights to Europe were expected to transport about 65,000 people.

Pan Am said it planned to fly its full schedule of 15 flights to Europe yesterday, with delays expected on three. All of its flights from Europe were operating, but with major delays. "They've been staggering in," said airline spokesman Merle Richman.

British Airways, another major carrier on the route, planned to operate 10 of its 13 U.S.-bound flights yesterday and 10 of its 13 flights to Europe. The airline hoped to restore full service today.

A TWA spokesman said that 11 instead of its usual 17 flights to the United States were operating yesterday, generally one to three hours late. Five planes from Paris and three from London -- all wide-bodied jets full of passengers --were among those arriving. A spokesman said the carrier planned to cancel one of its 17 outbound flights, a Dulles-to-Paris flight.

Yesterday's settlement of the Canadian job action came shortly after controllers in Australia and New Zealand dropped threats of similar boycotts that could have disrupted air travel in the South Pacific.

However, U.S. aviation still faces challenges from controllers in Portugal, Spain and, by some reports, the Netherlands.

The Portuguese, with a station in the Azores, direct flights along some secondary routes to Europe. Portuguese controllers say they will begin a boycott at midnight Saturday.

Transportation Secretary Drew Lewis said yesterday it might be necessary at that time to suspend U.S. traffic on the Azores routes; other transportation officials have said that any affected flights could be diverted into Canadian-controlled corridors.

FAA chief Helms said that Spanish controllers offered "sporadic" opposition yesterday to flights leaving for the United States, clearing one aircraft, but turning back a second. Lewis said some delays were experienced in airspace controlled from the Fiji Islands. Details were not available.

Meanwhile, the State Department continued contacting foreign governments to argue that this country's emergency traffic control system --staffed by supervisors, military controllers and nonstriking civilians --was operating safely.

The Canadian union, however, representing approximately 2,000 controllers, had cited 44 incidents of alleged safety violations as of Monday night, a week after the U.S. strike began. These and later alleged violations will be investigated by the 12 union-government teams.

Union president Robertson said yesterday that the two-day boycott had achieved its goals. "The safety questions that we raised are going to be given the attention they deserve," he said, adding that the public will be "able to judge for themselves whether they want to buy tickets on flights to and from the United States."

The union settled hours after the Canadian government began legal proceedings against individual controllers, suspended at least 29 and sent many others home. The agreement included no provisions to drop these proceedings, which are to continue in court next Tuesday. Maximum penalties are a year in prison and a $5,000 fine.

Earlier yesterday the Canadian government had reported that large numbers of controllers were abandoning the boycott, despite union instructions. However, Robertson said that the number of controllers who had broken ranks was "insignificant."

Meanwhile, about 150 supporters turned out in Brooklyn as Poli, who heads the Professional Air Traffic Controllers Organization, arrived at U.S. District Court to give his deposition.

Poli arrived a day late under threat of arrest by Judge Thomas Platt, who said he had reached "the end of my patience" when Poli failed to appear Tuesday, as instructed.

The Air Transport Association of America is trying to collect the $4.5 million from PATCO on grounds that the strike violates an injunction the association obtained in 1970 and has cost member airlines dearly. The association's lawyers questioned Poli in detail yesterday regarding his union's finances.

According to wire service reports, Poli contended that the union's $2.8 million in strike benefits is being held in a trust fund and, therefore, in legal terms is a liability, not an asset. As such, he said, the money cannot be seized to pay fines.

Poli's testimony came as a federal judge in Alexandria released Steven Wallaert, the last air controller still in jail for strike activities.

In Washington, meanwhile, Transportation Secretary Lewis said that airlines using airports covered by emergency "flow control" procedures were operating at about 76 percent of their normal schedule yesterday, the tenth day of the strike.

A total of 648 military controllers were on duty at FAA installations, Lewis said, with the number expected to rise to about 1,000 by the weekend.

Staff writer Martha Barnette contributed to this article.