United Nations and Washington eye each other closely. Each watches other's actions on UN finances and S. Africa

It could be one of the more substantive sessions that the United Nations has had in years. It will certainly be one in which the UN will be watching Washington, and Washington the UN. As the General Assembly convenes today, it will attempt to come to grips -- for the first time in the 41-year history of the UN -- with the organization's financial crisis and with internal management problems.

The second most important subject the UN must deal with is sanctions against South Africa. On this issue, the third-world nations, of which the UN is largely made up, and many Western states are sharply divided.

UN Secretary-General Javier P'erez de Cu'ellar has accused the United States of crippling the organization by withholding much of its financial contribution due this fall. The 159-member assembly must now decide how to remain solvent.

It must also determine how to deal with the controversial issue of internal reform. The US and a number of West European governments have accused the organization of irresponsible spending, and of permitting unmanageable bureaucratic growth.

A combination of US congressional cuts and proposed deferments could cut some 70 percent of the total amount that the US is required to pay the UN by October. The organization's single largest donor, the US underwrites 25 percent of the UN's budget each year. Its contribution is based on a complicated formula roughly dictated by gross national products.

If all of the proposed US cuts were to materialize, Washington would fall to fourth place among donor states. UN officials have charged this is a direct violation of Washington's treaty obligations.

Following a preliminary debate this week on South Africa's occupation of Namibia (South-West Africa), the session will begin next week with debate on the financial crisis.

The assembly will debate a report drawn by top-level experts of member-nations that calls for sweeping structural and budgetary reforms. The report, however, does not come to grips with the key question -- the desire of the major contributing nations for greater control over the UN budget process.

This has been a crucial US demand. And, according to Western sources, unless a compromise on the budgetary question is reached, the proposed reform package does not appear to have gone far enough to placate the US Congress, which is largely responsible for mandating US financial cuts.

There have, however, been indications that the Reagan administration is now favoring the view of its permanent representative to the UN, Gen. Vernon Walters. His view is that such drastic US action has already offended a number of key US allies and Washington is risking isolation among the UN's 159 member states.

In an effort to reverse at least some of the congressional cuts, Secretary of State George Shultz has sent letters to key congressmen, arguing that US influence, among friends and foes alike, could be undermined at the UN.

Implicit in Mr. Shultz's position is US concern over P'erez de Cu'ellar's position that he will not preside over a financially crippled UN. The US strongly supports him for a second five-year term. His first term expires at year's end.

If P'erez de Cu'ellar does not stand for reelection, an African would be next in line to hold the post. At a time of increased pressure on the US and its allies for comprehensive sanctions against South Africa, the Reagan administration would like to avoid having an African elected to the post.

According to African sources, members of the UN that are also members of the 101-nation strong ``nonaligned'' movement will seek UN Security Council endorsement for a package of sanctions against South Africa. The nonaligned nations are looking for sanctions similar to those in the US congressional bill and in a package adopted by the Commonwealth.

If the US and Britain veto the nonaligned's package, the issue will most likely be brought before the Security Council again. The second time it would appear in a proposal for selective sanctions that is expected to pass.

Meanwhile, President Reagan is expected to veto the sanctions bill sent to him by Congress last week. If, as is also expected, his veto is overriden, there will certainly be implications at the UN.

``If he cannot veto sanctions approved by the US Congress,'' one African delegate said, ``can he, in good faith, call for a veto of a sanctions package agreed upon by nearly all the United Nations' member-states?''

According to one Western source, ``The importance of what happens in the US Congress cannot be underestimated. . . . We will be watching Washington, and they'll be watching us. There's an implicit irony that the United Nations and Washington, like two terrible twins, will become almost symbiotic over the next three months.''

When President Reagan addresses the General Assembly next Monday, it is hoped that one of the twins' intentions will become a bit more clear.