After two months of direct intervention in Afghanistan, the Soviet Union faces stark choices about its role there and its relations with the rest of the world. The United States, in reaction, faces important choices of its own.

The Soviet-backed coup and ground invasion last Dec. 27 began a period of sweeping change in U.S. policy toward the Russians. What a senior policy-maker calls "the crescendo of crisis" is now diminishing. Moscow and Washington are assessing what has taken place, and looking ahead to the spring and beyond.

From the Washington perspective the venture in Afghanistan, always considered difficult and costly, has fared even more poorly for the Soviets than anticipated. Behind the daily headlines and intelligence reports are, in this view, two underlying facts that spell trouble for the Russians.

First, it is clear that the large and well-equipped Soviet expediationary force has been unable to intimidate or quell the Afghan resistance, which continues to grow. Last week open defiance of the Soviets spread from the countryside to the capital of Kabul and other cities, in a six-day general strike impressive effectiveness.

The Soviets, as a result, continue to build up their expeditionary force and to dig in for a long haul. The initial invasion force of 50,000 troops has now grown to 75,000 within the country plus 25,000 in staging areas along the border. Another Soviet brigade crossed the border last week. U.S. analysts report additional units being mobilized in the Russian rear, and they guess that the total Afghan and border area force of the U.S.S.R. will reach the neighborhood of 150,000 troops by early spring.

According to intelligence reports in the hands of high officials, the Russians are constructing permanent facilities within Afghanistan, acquiring land for living quarters and military clubs, setting up a Soviet radio station in Kabul, laying cables for communications in other areas and drilling wells for water during the dry summer months.

Second, and possibly even more serious for the Russians in the long run, is the failure of the Soviet-installed Babrak Karmal government to win popular respect or support. A symbol of this failure, in Washington's eyes, is that Babrak is reported to have taken refuge in the heavily guarded Soviet Embassy during last week's fighting in Kabul because his presidential palace was considered unsafe.

Creation of a respectable political leadership in Kabul is essential to the Russians. It is a necessary first step toward the vital task of rebuilding the still crumbling Afghan army as well as a precondition for internal stability and international recognition. Babrak is not taking hold, and new or additional leadership is nowhere in sight.

The almost total absence of a political base within the county is among the reasons that Afghanistan 1980 is proving to be more complicated that Hungary 1956 or Czechoslovakia 1968. The Eastern European states, modern societies with cohesive institutions, had been under Soviet control since World War ii. There was in each case at least a major faction of the existing Communist Party that accepted the Soviet invasion and served as the instrument of Soviet power. In Afghanistan, political acceptance, to say nothing of support, is minuscule.

In these bleak circumstances the Soviets are, in the view of U.S. experts, confronted with limited options regarding the near future in Afghanistan:

When the snows melt and operations become easier, the Russians could undertake all-out military action this spring and summer to fasten tight control on the cities, pacify or destroy uncooperative villages and take the war to rebel tribesmen in mountain redoubts. This probably would require a much larger force, at least 200,000 to 250,000 men, and the unrestrained use of military power in an attempt to clean out Afghan resistance once and for all.

The Soviets could use a more limited force, perhaps the expected 150,000 or so, to secure the main highways, garrison the main cities and mount occasional raids against oppositions centers and rebel tribesmen. This strategy would rely on symbols and examples of military power more than on its all-out application.

Perhaps after an initial show of force, the Soviets could adopt a long-range, more gradual strategy for wearing down the opposition and spreading a secure base, on the Afghan equivalent of the Vietnam "oil spot" strategy. If the Russians were patient -- and if they were able to build political support and rebuild the Afghan army -- they conceivably could control the country with a smaller Soviet garrison, permitting some of their troops to go home.

There is little or no expectation in official circles here that the Russians would consider pulling out or ever substantially reducing their presence until after a spring-summer campaign to establish control and make as many gains as possible against the insurgency. tOnly after the Soviets crush the opposition, or establish a long-term strategy pointing to effective control, would they be seriously interested in withdrawing most or all of their forces in a "neutralization" agreement with the outside world, in this view. Even then, such a possibility is considered doubtful.

Soviet President Leonid Brezhnev's recent statement that Soviet troops would begin to withdraw after "all forms of outside interference" are terminated is seen here as an attempt to reduce, the international heat, rather than the start of a genuine "neutralization." In keeping with the greater-than-expected difficulties within Afghanistan, the Brezhnev offer was more tentative, limited and muted than the "peace offensive" overture that had been expected from Moscow.

The Brezhnev offer says, in effect: neutralize Afghanistan and then we'll get out. The U.S. counter-offer, expounded by the Carter administration last week and to be embellished Monday by Secretary of State Cyrus R. Vance, says, in effect: get out first, and then neutralize Afghanistan.

A European offer, put forward by the British foreign secretary, Lord Carrington, and other European ministers, is a more ambiguous call for "a neutral Afghanistan to be outside competition among the major powers." U.S. officials profess to be happy with the general thrust of the Carrington initiative, which is interpreted here as an attempt to put Moscow on the defensive.

The U.S. idea, as explained by its exponents, is "to keep the pot of gold at the end of the rainbow" for Moscow agreeing in principle to a neutral and independent future Afghanistan under negotiated arrangements. At the same time, the United States is determined to keep the onus of military intervention on the Soviet Union as long as the Russians persist in the occupation, avoiding diplomatic signals that would tend to dissipate the widespread international antipathy to Moscow's action.

In this pursuit, State Department officials emphasized yesterday that the withdrawal of all Soviet troops is an "antecedent" to a neutral Afghanistan, but that talks about the country's future status can proceed in present circumstances. Such discussions with the Soviets are beginning through ambassadorial channels and may continue at a meeting of Vance and Soviet Foreign Minister Andrei Gromyko if they are present together at a funeral for Yogoslavia's President Tito.

The diplomatic talk, as seen here, will be for show rather than for real in the foreseeable future. The main arena is expected to be the war zone rather than the conference table. Every military decision in the Kremlin will have its repercussions both within Afghanistan and in international opinion as long as reporters, diplomats and intelligence agencies are able to observe and spread the word.

The U.S. activity that can affect the course of military action most directly is the covert, and controversial, supply of weaponry to rebel tribesmen fighting the Russians in Afghanistan. American officials insist that this supply is not a large factor in the Afghan situation, since the rebels are said to amass far more weaponry from defecting Afghan army troops, from captured or abandoned stores and from Islamic allies than from the United States.

Nonetheless, officials concede that the Russians may believe the U.S.-supplied arms are the source of much of their trouble. The Carter administration's ability t adjust or cut off the arms flow gives it a potential lever if real negotiations are ever in prospect.

Beyond the focus on Afghanistan, both Moscow and Washington are faced with a variety of questions and options in the uncertain period ahead. For both countries, the choices are affected by the present stage of the political succession processes -- the subterranean positioning for post -- brezhnev power in Moscow, and the open contest for the presidency in the United States.

The superpowers must decide how to respond to one another at many levels:

Strategic competition, in the acquisition, deployment and testing of nuclear arsenals sufficient to destroy each other's society. How will they handle the negotiated but unratified stratefic arms limitation treaty (SALT II)? Will unbridled competition destroy any chance for negotiated controls? What will be the effect of unrestrained competition on national budgets and on the efforts to restrain other nations from joining the nuclear arms race?

Regional competition in Southwest Asia, where the United States is seeking to contain Soviet power in order to forestall domino jitters and secure the oil supply of the Persian Gulf so vital to the West. And in Southeast Asia, where a Vietnam-Cambodia-Thialand conflict could bring in China and possibly the United States, and eventually a major Soviet counterstrike to the rival Chinese.

The United States is tempted to "draw the line" freely against the Soviets in order to stave off advances or encroachment. But a recent visitor to the U.S.S.R. reports the Russians as determined to choose their ground carefully but then not to retreat, U.S. security "guarantees," so casually given during most of the post-World War ii era, could be actually tested in unexpected and dangerous fashion.

Political competition in Europe, the Islamic world and the uncommitted states of the developing world. The Kremlin will have to decide whether, among other things, to continue the crackdown on its most prestigious and famous dissident, Andrei Sakarov, despite the heavy political costs in Europe. U.S. political and economic cooperation worldwide has become even more important even while becoming more difficult due to electioneering and economic troubles at home.

Because of the Soviet action in Afghanistan is different in so many respects from anything else in the three decades of intensive U.S.-Soviet confrontation, the United States has little historical experience for its decisions. Moreover, the United States has never Before been deeply involved or concerned about Afghanistan, Pakistan or that broad area almost exactly half-way around the world.

The Russians have richer experience. On Nov. 21, 1864, Czar Alexander II's foreign minister, Prince Gorchakov, summed up his country's activities with the nomadic populations of central Asia where Russian military operations recently were carried out. To protect her borders, the state had been forced to advance, only to be confronted with new resistance from new forces.

"The state thus finds itself forced to chose one of two alternatives, either to give up this endless labor and to abandon its frontier to perpetual disturbance . . . or to plunge deeper and deeper into barbarous countries, where the difficulties and expenses increase with every step," Gorchakov wrote. The greatest difficulty, he concluded, "is knowing when to stop."