An international tribunal established to judge both governmental and nongovernmental United States and Iranian claims against each other is slowly groping its way toward becoming a well-oiled, efficient machinery.
But mutual suspicion on the part of the litigants and differences in interpretation of the accords of Algiers, which paved the way for the release of the US hostages from Iran, are likely to keep the nine members of the tribunal on the alert.
International arbitrators describe the Iran-US Claims Tribunal as ''unprecedented'' in both amounts of money spent and numbers of claims involved. Many of these arbitrators, among them members of the Iran-US Claims Tribunal, which is based in The Hague, the seat of the Dutch government, were here last week to participate in a symposium organized by the Stockholm Chamber of Commerce -- the contractually appointed arbitrator in most East-West trade contracts and many other international commercial deals.
''We look forward to a friendly arbitration,'' says Swedish Judge Gunnar Lagergren, president of the Iran-US Claims Tribunal. The tribunal further consists of three US judges, three Iranian judges, and two other jurists from neutral countries -- a Swede and a Frenchman. ''I applied the term 'friendly arbitration' when I was involved in the Indian-Pakistani conflict,'' Judge Lagergren adds. ''It worked there while the two countries were fighting a war. It will also work here.''
Despite Judge Lagergren's optimism, a good number of problems have yet to be resolved. The tribunal began hearings March 9 in The Hague's Peace Palace on four unresolved issues of principle:
* A dispute over what to do with interest earned by the $1 billion deposited by Iran with the Nederlandse Bank BV, the Dutch central bank, as a security for paying awarded claims. Iran is demanding that this interest, which could exceed government. But the US wishes to see the interest added to the security account as was the case with Iranian escrow accounts at the Bank of England during the hostage release.
* When a claim is settled out of court, whether it should be paid out of Iran's $1 billion escrow account, and under what circumstances. Tribunal members say the issue here is to what extent the tribunal is to take responsibility for settlements not made under its auspices.
* Payment of the expenses incurred by the Dutch central bank.
* Indemnification of possible claims against the Dutch central bank for its handling of the escrow account.
Tribunal members do not believe that resolution of these issues will obstruct court proceedings to judge the approximately 5,000 claims submitted to the tribunal before the Jan. 19, 1982, deadline. But a possible bone of friction involves the question whether this deadline applies only to claims by individuals and corporations or also to government claims -- a question tribunal members still hope will not arise.
''These 5,000 (already submitted) cases fall into different categories,'' says Howard M. Holtzman, chairman of the American Arbitration Association and a member of the Iran-US Claims Tribunal. More than 4,000 of the 5,000 claims range from small companies which suffered losses, to individuals who ''had to leave their cars and refrigerators behind,'' according to Mr. Holtzman. Of these smaller claims 3,000 are US claims against Iran and approximately 1,200 are Iranian claims against the US.
Most of these cases, which involve sums under $250,000, will be presented to the international trade tribunal by the US and Iranian governments on behalf of their citizens or companies. The claims of governments and larger corporations total billions of dollars. The members of the tribunal have as yet no precise overview of the sums of money involved. Crates filled with Iranian claims, filed in 24 copies -- 12 in English, 12 in Farsi -- at the last minute, still stood unopened in the Peace Palace last week.
Among the claims, however, is a larger than $11 billion Iranian government demand resulting from military equipment ordered and paid by the regime of the Shah but never delivered. The US Supreme Court has decided to refer claims filed by US companies in front of US courts to the international tribunal in The Hague. Some of these claims involve substantial figures:
* SEDCO: $175 million for unilateral appropriation of 16 drilling rigs and assorted construction equipment.
* Santa Fe International: $168 million for expropriation of drilling equipment and breach of contract.
* Xerox: $84 million for nationalization of Rank Xerox Iran.
* American Telephone & Telegraph: $69.6 million for breach of contract regarding a telephone system ordered by Iran.
* General Motors: $58 million for nationalization of 55 percent of General Motors Iran and unpaid passenger car kits sitting in a General Motor's stockyard in Canada.
Tribunal judges expect Iran to raise, depending on the claim, one of several counterarguments. Iran charges that US companies breached their contracts by pulling out before the Nov. 4, 1979, occupation of the US Embassy in Tehran and in some cases, even before the fall of the Shah. Other contracts, Iran claims, are the ''unlawful product of corruption.''
The international tribunal will split up into three separate chambers consisting of one American, one Iranian, and one neutral member. Its proceedings will be confidential, although the awards are expected to be made public. Priority will be given to the judgment of claims on a case-to-case basis.
Iran has asked the tribunal for a period of six months to file its defense in some cases. ''Iran, being the main defendant, quite rightly states that a lot of necessary documents have been destroyed during the revolution and the Gulf war, '' said one judge. This judge further pointed out that Iran has a ''scarcity of qualified lawyers.'' Iran is due to file its first statements of defense toward the end of this month.
Tribunal members are confident that both the US and Iran take its work seriously and will regard its decisions as binding. But the Iranians are said to be somewhat suspicious. ''They (the Iranians) lack the experience of American lawyers who constantly litigate,'' said one tribunal member, adding that ''they are simply afraid of American tricks.''