Ostensibly it was a mild surprise, an unexpected appointment: Robert S. Struass, former chairman of the Democratic National Committee, would be the Carter administration's special trade representative. The White House confirmed the appointment late last month, and announced if formally Friday.

Behind that announcement lay a juicy political tale - a story of hopes raised and abandoned, intensive lobbying by many interest groups, accusations of political betrayal and a lot of wounded pride. The job of special representative for the trade negotiations - a potentially powerful position little understood outside the economic community - proved a difficult one for the new President to fill.

Orville L. Freeman, former governor of minnesota and Secretary of Agriculture, wanted the job and thought for a while that it had been offered to him; Freeman was eventually vetoed by the AFL-CIO. Former Rep. William J. Green, the unsuccessful Democratic candidate for senator from Pennsylvania last November, also hoped for the appointment, and thought for a time he had it, but Green's closeness to the AFL-CIO and a lack of enthusiastic support from other power brokers did him in.

President Carter personally called John T. Dunlop, the Secretary of Labor for part of the Ford administration, to offer him the job. Dunlop was organized labor's first choice for this post, as he had been for Secretary of Labor. Dunlop was interested in the latter, but he didn't want to be special trade representative.

Four or five others, mostly trade experts, were considered for the job. One of them, business consultant Harold Malmgren, might have had it if he had been willing to give up his lucrative private consulting firm, but he wasn't.

So the White House turned top Strauss, a jovial, millionaire-lawyer from Dallas - the man who picked up the pieces of the Democratic Party after its humiliating defeat in 1972 and helped produce victory in 1976.

This reconstruction of how Strauss got his new job is based on more than a dozen interviews with persons directly involved and their intimate associates. All ask not to be identified.

The idea that Strauss might become special trade negotiator first came up soon after the November election. The President-elect mentioned it to him once or twice, as did friends on Capitol Hill who thought Strauss was well suited for it. Strauss didn't agree at the time, though he was tempted. He though it was an important post.

The job is one of potential power and influence, thus far not realized. The special trade representative is in charge of negotiating multilateral agreements with other countries, and by statute he is the executive branch's principal official on all trade matters. Experts say a strong trade representative could develop influence on East-West trade international food policy and other issues.

Strauss knew little of these matters, thought some of them interested him. He told friends the one job that could surely tempt him was Secretary of the Treasury. Failing that, he would practice law and make money. The Washington office of his Dallas law firm was preparing for that eventually; it had doubled in size to about 35 lawyers over the past year or two.

W. Michael Blumenthal got the Treasury post. A veteran of trade negotiations himself, Blumenthal apparently assumed he would have an influential voice in the choice of the trade representative. He began assembling names of possible candidates.

Carter's principal lieutenants decided at meeting on St. Simon's Island, Ga., between Christmas and New Years that they would have to pay special attention to the trade job, because so many interest groups were eager to influence the choice. Hamilton Jordan, Bert Lance and others quickly learned its senstitivity.

The problem they faced briefly, was this: differently elements of society - and different factions within the coalition that elected opposed views on American trade policy.

Big labor, the steel industry, the shoe industry, the domestic television industry and others think the United States must raise tariffs to protect its domestic economy - and their livelihoods. They argue that foreign countries unfairly subsidize exports to the United States which undercut domestic products.

The multinational corporations and agricultural interests favor unfettered free trade, which they feel is best for them and for the country. They are supported by old-line "free traders" in the liberal wing of the Democratic Party.

"This area is very heavily lobbied" one of the participants in this drama observed. "Everybody gets excited about it - including people who main high-priced lobbyists in Washington to influence decisions like this one."

In early January, soon after the meeting on St. Simon's Island, Blumenthal met with Orville Freeman and asked if the would take the special trade representative job. Freeman said he would, provided he became one of the adminstration's sendior economic adviser saw well.

"He's a proud man," one of Freeman's friends observed. As a former Cabinet members, he wanted to be sure he would have visibility and influence as trade representative. Blumenthal indicated that he could give Freeman what he wanted, but Freeman and his friends later though perhaps this was something only Carter could have done.

Immediately after the inauguration, Vice President Mondale toured Europe and Japan. A many stops he was pressed on trade matters which trouble America's allies deeply: when would Carter name a trade representative. Mondale was asked, and when would the stalled Geneva negotiations get along?

(The Europeans and Japanese are still nervous about the strength of the current economic recovery, and they are fearful that some countries - even the United States - will revert to protectionism and set off a round of destructive tariff increases that will reverse the recovery abruptly. The Geneva talks, they hope, will prevent this from happening.)

Mondale told Carter of the intense interest in this appointment when he returned. Carter then asked him to take over the task of finding the right person for the job.

Freeman's backers thought Mondale was sympathetic to their man, a fellow Minnesotan and old friend. Hubert H. Humphrey was one of Freeman's strongest supporters, and he was also Mondale's political mentor.

But labor opposed Freeman unequivocally. Lane Kirkland, secretary-treasurer of the AFL-CIO, told the White House that the political cosgs of picking Freeman would be extremely high. Labor regarded him as a freetrader, and a friend of both farmers and multinationals (whom Freeman now consults in private business). According to one source, the AFL-CIO's leaders also found him personally objectionable.

Labor thought Mondale's was sympathetic to its position. The AFL-CIO's first choice was Dunlop, and Carter himself offered the Harvard economist the job. When he declined it, labor said former Congressman Green was its choice. Some labor leaders - particularly those in the garment trade unions, which are extremely upset by cheap imports - thought Mondale had heard their pleas for Green sympathetically.

But Mondale and others in the White House found that interests outside labor wouldn't accept Green. "They thought he was in labor's hip pocket," as one participant put it. Green's associates concluded that labor's support was simultaneously his best asset and his budget liability.

So the first two leading contenders were knocked off. For a time others were considered: William R. Pierce, another Minnesotan, an officer of the Cargill grain company and a former deputy to the trade negotiator; Will Leonard and Daniel Minchew, members of the International Trade Commmission; Myer Rashish, a veteran of earlier trade negotiations and the Kennedy White House; Malmgren, former deputy special trade representative and a man with influential friends in labor, industry and Congress.

Only Malmgren survived the selection process, but - recently divorced and anxious to make a success of his new consulting business - Malmgren wasn't interested.

As the attempt to find someone for the job dragged on, one interested but frustrated onlooker was Sen. Abraham A. Ribicoff (D-Conn.). Ribicoff was both an author of key trade legistration, and a close friend and admirer of Bob Strauss. He talked to Strauss several times about the importance - and the desirability - of the job.

But by February Strauss had set off in another direction. He had taken on new clients at the law firm, and accepted election to the boards of Xerox and Brandiff.He was still interest in the trade post, but didn't see how he could take it.

But by mid-February, Jordan, Mondale, Lance, and others in the White House had decided they didn't know what they would do if Strauss didn't take it. They had no other plausible candidate, and the job had to be filled.Ribicoff, Sen. Russell Long (D-La.), Malmgren and many others kept telling them that Strauss would be a great choice - that his political skills and support on Capitol Hill would be invaluable assets. ("He could learn what he didn't know about trade later, that was no problem," one ally said.)

On Feb. 23 Carter called Strauss to the White House and asked - "in a very low voice," Strauss remembers, "but it was exceedingly firm and persuasive" - to take the job. Carter asked for an immediate reply, but Strauss said he would need a day or two to think about it.

During that day or two Strauss talked to Long, the unpredictable chairman of the Senate Finance Committee. Long told Strauss a man should be aware of his options, then outlined the two he though Strauss faced: either he could take the job, make a success of it and be a hero; or he could turn the President down, in which case, Long promised, "we'll run you out of town."

"Russell," Strauss replied, "you've explained it even clearer than the President did."

So Strauss took the job. Some of Green' labor supporters still feel Mondale betrayed them. Freeman's allies also question the Vice President's real efforts on their man's behalf. Blumethal, failed to influence the apointment. Many of the unsuccessful candidates still believe their credentials were given short shrift in the White House. But the Carter administration has a trade representative with a lot of friends - even if it has avoided the question of what policy he should pursue.