The third round of indirect bargaining between the United States and Iran over terms for release of the 52 American hostages has begun with officials in both Tehran and Washington saying privately they are uncertain whether any binding agreement can ever be reached, even if the current process continues.

The gulf today between the two countries thus seems enormous. But it is nowhere near as great as it once was, when the Iranians were demanding return of the shah, himself, and the United States was saying it would not discuss any matter until its people -- taken in an internationally recognized illegal act -- were returned.

Iran's Prime Minister Mohammed Ali Rajai still can't even look like he is negotiating -- though in fact he is -- because the Maijlis, Iran's parliament, supposedly is the only government body that can set the terms of release. That's because Ayatollah Ruhollah Khomeini said it would be that way.

Khomeini, in fact, did set down the framework for the current bargaining last Sept. 12, with his four conditions: the United States would pledge not to interfere in Iran's internal affairs; the U.S. president would unfreeze Iran's assets; he would remove all claims against Iran, and he would order the return of the shah's wealth.

Those are still the main conditions and both countries say washington has agreed to them "in principle." The problems come in trying to work them out in detail:

1. Noninterference. Up to now, the Iranians have said this condition has been met satisfactorilly through statements by President Carter and Secretary of State Edmund S. Muskie. Now the Iranians have said, in their latest statement, that they want the American response to "accurately tally" with what the Majlis proposed.

The Majlis opened this condition with the phrase, "Due to the interference of the United States in the internal affairs of Iran. . . ." This looks like Iran may again want some U.S. acknowledgement of, or, worse, an apology for, past activities in Iran. Carter has refused any form of apology in the past.

2. Unfreezing Iranian assets. Ten days after the hostages were seized, and shortly after Abolhasan Bani-Sadr, then Iran's finance minister, now president, threatened to withdraw all Iran's money from U.S. banks, Carter ordered all Iranian assets in the United States and in American banks abroad frozen.

Involved was more than $8 billion worth of gold, U.S. securities, bank deposits, military equipment, oil revenues and assorted assorted other holdings.

Iran now calculates these assets involve $11 billion.

The U.S. Treasury order on Nov. 14, 1979, establishing the regulations for the freeze permitted U.S. banks to take from the Iranian deposits in their banks an amount equal to the outstanding Iranian loans that went into default once the freeze began. These so-called"set offs" mean that several billion dollars of Iranian money have been absorbed by U.S. banks.

Since the banks were given that privilege, the Treasury order also permitted American corporations and individuals who believed they were owed money by the Iranian government to file legal claims and seek to get legal orders called attachments against the frozen funds. Attachments, once approved by a court, require the funds involved to be held by the court until a final judgment is made on the original claim. If the claim is aproved, the amount awarded is taken from the funds attached.

More than 300 claims have been filed in U.S. courts and attachments sought against an estimated $6 billion of the frozen Iranian assets.

The president has the power at any time to rescind his freeze order. The problem for the Iranians is that once the president's freeze is lifted, the pending legal claims against that money could keep it here for years until the claims are settled.

The Iranians recognize this problem and have now said the president's word is not enough; they want the frozen assets transferred to Algeria's national bank. That, of course, does not indicate what is to be done with other frozen assests -- such as military equipment -- which cannot be held in a bank.

It's clear the Iranians have now linked the frozen Iranian assets with the U.S. claims. In Iran's first proposal, the assets were to be returned directly and immediately to the government of Iran for its use. The latest public position has the assets transferred to Algeria and investigation of all claims proposed in connection with an "arbitration" process.

3. Cancel all legal claims against Iran. Iran at first demanded the president use his power to set aside all the claims, something they had been told he could do under U.S. law. Some State and and Justice Department lawyers have agreed that is possible, as have Iran's own U.S. attorneys. Whether the president would do it is another thing. What is clear, however, is that some, if not all, of the claimants could and probably would oppose such an action in court -- and that could hold things up for a long time.

The newest Iranian proposal seems to be leading toward an international claims settlement commission. Such bodies have been set up in the past, but the cooperation of the claimants, and probably Congress, would be needed to get it done in this situation.

Right now, the U.S. government's lawyers have filed in every court handling an Iranian assets case for delays in proceedings until the negotiations are settled.

A still-ticking time bomb in all this is Iran's repeated demand that the United States take care of any claim filed against Iran by the hostages or their families. Tehran wants the United States not only to defend against such suits but also to pay whatever awards are eventually made.This one looks impossible for any U.S. president to accept -- though there are precedents for such an action.

4. Return of the former shah's wealh. This one has gone up and down on the difficulty scale, probably because it has the most political volatility in Iran. At first, Iran wanted the president to recognize the nationalization of the assets of the shah and his family, then seize whatever property they had in the United States and transfer it back to Iran. Now it appears Iran wants Washington to give "guarantees" to Algeria, apparently in the form of some type of deposit. When an asset is located, the Iranians would withdraw an equal amount from the holding in Algeria -- leaving the United States, apparently, to get back its money by taking possession of the asset.

The U.S. position has been that it would try to locate assets of the shah and his family, and assist in any Iranian court attempts to get control of them when found. The new idea appears impossible to accept, and some U.S. officials familiar with Iran see it as a negotiating ploy by Iranian officials, designed to keep some hardliners off their backs with a tough new approach, while they atempt to work out the other issues.