When Robert S. Strauss was named President Carter's special trade representative last February, even his best friends were surprised. There was no doubt the 59-year-old former Democratic National Committee chairman, who successfully led the party out of the McGovern defeat of 1972, was a shrewd and skillful politician. The worry was, what did he know about international trade?

Today, six months after Strauss formally took over as chief trade negotiator, there are those who still shudder over his pragmatic, often flamboyant, approach. But few dispute his success so far, either in negotiating with other countries or in his dealings here at home.

In a relatively short time, the fast-talking, grayhaired Dallas millionaire has doused most of the potentially dangerous brushfires in import-injured industries such as footwear and television set manufacturing, diffused protectionist pressures in Congress, and calmed the fears of European and Japanese trading partners.

As a politician, Strauss has kept his hand in domestic matters by taking on sensitive outside assignments for the President - accomplishing them so well that he's being mentioned as a possible successor to budget director Bert Lance (Strauss has told friends he doesn't want the job, but he doesn't deny he'd take it if pressed).

Most important, he has gotten the long-stalled multilateral trade negotiations - the so-called Tokyo Round trade talks that have been a primary goal of U.S. trade policy since the Nixon administration - finally off the ground. The negotiations had been at a statemate since mid-1973, when they broke down in the face of the Arab oil embargo.

"Strauss has learned the substance remarkably fast, and he's been extremely skillful in striking a balance between domestic political needs and international acceptability," says Harald B. Malmgren, a respected trade negotiator in the Kennedy, Johnson and Nixon administrations who himself was a sometime competitor for the job Strauss now holds.

Isaiah Frank, the Johns Hopkins University professor who shepherded the aggressive free-trade-with-safeguards policy that launched the Nixon administration on a new international economic venture, agrees. "He seems to have considerable flash and ability to persuade," Frank says of Strauss. "I don't find anything to be critical of so far."

The only major complaints seem to come from classical free-traders, who argue that Strauss may havebowed too often to protectionists in his efforts to deal with short-term problems. But here, too, the grumbling is muted. "I think he's paid a little more ransom money than he's needed to," says Rep. Henry S. Reuss (D-Wis.), the liberal chairman of the House Banking Committee. But, Reuss adds, "He's diffused the pressures on the Hill - and that's important, too."

To some analysts, Strauss' performance is best measured against the situation that existed when he first took office. Both business and labor were clamoring for protection from imports in several key industries. Protectionist sentiment was mounting in Congress to the point where many officials seriously worried about the administration's ability to conduct trade policy. And the Tokyo Round talks seemed hopelessly stalled.

Strauss began tackling the problem by starting with Capitol Hill, where he had dozens of longstanding contacts, pleading with key congressmen to hold off on any new legislation to give him time to bargain. He also started keeping the lawmakers up to date on the details of all his negotiations. When he worked out a deal with a foreign country on any particular import problem, he went personally to the Hill to sell it himself. The strategy was successful. Exults Sen. Russell B. Long (D-La.), chairman of the Senate Finance Committee and a longtime Strauss friend: "We have a man in charge of our trade policy who we . . . in Congress can trust."

The new trade chief then focused on those U.S. industries most vocal in their demands for tariffs and quotas. The newly revamped U.S. International Trade Commission, which reviews petitions for import relief from industry, had recommended stiff tariffs or quotas for shoes and color-TV imports, and appeared likely to extend that remedy to other products in what administration officials feared might become a pattern.

Strauss' solution was to dredge up a device called the orderly marketing agreement - or OMA, in economists' jargon - a pact between the U.S. and a foreign nation in which the other country agrees to limit its exports here voluntarily for a specified period of time. The mechanism was used by the Ford administration to fend off pressures for quotas on steel. It still is a form of protectionism but, Strauss insists, is not as bad as quotas.

Within a few months, Strauss had persuaded Taiwan and South Korea to trim their exports of cheap shoes, and cajoled Japan into cutting back its shipments of color television sets to the U.S. - both on pain of possible mandatory quotas if they refused. The move was opposed by free-trade advocates within the administration - including Charles L. Schultze, the President's chief economist, and W. Michael Blumenthal, the Secretary of the Treasury - but Strauss won out.

Perhaps Strauss' most spectacular achievement, however, has been to revive the multilateral trade negotiations. The talks had been bogged down so badly that when the seven-nation economic summit decided last May to provide "new impetus" to the bargaining, the promise was greeted with more skepticism than any other the leaders offered. Protectionist feelings still were running high, both here and in Europe, and the prospects appeared grim.

Strauss worked quietly behind the scenes, however, assuring nervous Europeans that the U.S. first "didn't want to break up" their long-cherished Common Agricultural Policy; and arguing that the same conditions which they contended were blocking a reduction in trade barriers actually cried out for more liberalization. The old Texas smooth-talk worked. By mid-July, Strauss and the Europeans had agreed on a four-phase plan for moving the talks ahead that was hailed as a major breakthrough.Although there has been some slippage since then, the schedule still is intact.

It was Strauss' use of the orderly-marketing-agreement mechanism that got him in the most trouble with his critics. While industry and labor generally have accepted the compromise grudingly, liberals have been upset that the ploy has been too protectionist. Reuss, for example, complains that the voluntary quotas imposed under the OMAs have hurt consumers, too, by raising prices that buyers pay for goods where there is reduced foreign competition.

Strauss assured reporters in June that the shoe agreement he struck then would be the last such OMA the administration would seek to negotiate "for the rest of the year." How long that promise will stay intact remains to be seen.

In fairness, Strauss' performance has not always favored the protectionists. After the U.S. Steel Corp. tried to make an end run last June around his own negotiation efforts, Strauss shattered longstanding custom by bluntly denouncing the company's action as "an outrage." He alos has pressed Japan for support in pushing through a sharp reduction in trade barriers worldwide.

Strauss resolved problems about his lack of knowledge about the trade matters early in his tenure by decreeing that everything be spelled out so he could understand it. After a month of nodding bleary eyed as lawyers explained complex trade concepts, the trade chief stood up calmly and confessed he hadn't been able to grasp them. "I think I could understand Einstein if he explained himself in simple terms," he said. "Why don't you see if you can do the same?"

His manner to foreign officials has been no less direct. Once he left flustered a group of staid Japanese trade envoys by coaching them, as though they were party ward-workers, on how to deal with Congress. "You've got to throw us a fish or two so we can respond with something ourselves," he said. There was no indication whether the advice ever was heeded.

Although the trade negotiator's post technically is far removed from domestic politics, Strauss has maintained Carter's confidence as a political adviser by taking on outside assignments that less-experienced White House aides were unable to handle.

The Texan played a key role, for example, in formulating administration policy on the handling of illegal aliens, and then took on the job of working out a "compromise" on the controversial cargo-preference bill (Strauss' recommendation: Back a stiff U.S.-flag requirement, despite criticism that it would be bad economics, because the President promised it in the campaign). His latest assignment is as the President's chief behind-the-scenes salesman on the Panama Canal issue, helping to armtwist reluctant senators into voting to ratify the treaty.

Last week, the trade chief completed a round of overnight trips, first to Ottawa to discuss the pending Tokyo Round talks, and then on to an international businessmen's conference to sell U.S. policy. Monday he leaves for another European tour, to Brussels, Bonn, Paris, Rome and back to Brussels again.

Strauss' own assessment of his performance is characteristically immodest. "I'm beginning to master this job pretty well," he says. "I think I've learned a thing or two." After six months of Strauss' stewardship over trade matters, there still are a good many critics who might take issue with that appraisal. But the number who would dismiss it entirely is steadily diminishing.

If Strauss ultimately is named successor to Lance, as some speculation now has it, no doubt there will be renewed questions - this time, perhaps, as in the case of fellow-Texan John Connally's appointment as Secretary of the Treasury in the Nixon administration, can Bob Strauss add?

Strauss probably would concede that he can't - at least in terms of knowing the intricacies of federal budget making. But Strauss supporters argue on the basis of his past performance that, after the first six months in office, it may not really matter.