Virtually everybody involved directly or indirectly in the Falklands war finds themselves in a Catch-22 situation.
This is even so for British Prime Minister Margaret Thatcher, although the first few days of fighting have gone so well for the British that her government says the choice now for the Argentines is between surrender and complete British occupation of the islands.
Ironically, the more resounding any British victory, the greater could be some of Mrs. Thatcher's eventual problems at home as well as abroad.
The United States, caught between its Atlantic/European and American hemispheric roles, is in the most frustrating position of all. This is because, despite overwhelming power, Washington cannot use it without putting at risk one or the other of those roles. The result: The US for the moment can do little more than urge restraint from the sidelines - albeit recognizing the principle Britain is defending.
US Secretary of State Alexander M. Haig Jr. has said that the rule of law must be supported. He added that if it broke down, other dangerous situations could develop in the hemisphere.
Mr. Haig was not more specific. But the most obvious possible situations are those likely to follow if Venezuela and Guatemala (both Spanish-speaking) resorted to force in pursuit of their respective claims to parts of Guyana and Belize (both English-speaking).
Awareness of this was presumably behind Mr. Haig's implied hint to Britain to consider returning to the negotiating table, short of outright military victory, now that the British hand has been immensely strengthened by establishment of a firm beachhead at Port San Carlos.
But here one runs straight into Mrs. Thatcher's dilemma. British public opinion has been strengthened in its support of her, now that the initial phase of the British military operation has gone so well.
Given the domestic mood, the British prime minister would be in deep political trouble reaching far beyond the hard-line right-wing fringe of her own Conservative Party if she were now seen to be willing to compromise by conceding in the least degree on Argentina's claim to sovereignty over the Falklands.
(There is also the problem of how long Britain could afford effectively to defend the Falklands against some future Argentine or other attack, if the islands are returned to total British control in the current military operation.)
Yet if Mrs. Thatcher presses on for complete Argentine military surrender, she puts at risk the support and goodwill Britain has hitherto gotten from her most important allies - the US and her European partners - in the Falklands crisis.
Should the US decide that American interests are best served by compromise before complete humiliation of Argentine junta leader Gen. Leopoldo Galtieri, and should Mrs. Thatcher refuse to go along, the hitherto warm relations she has had with the Reagan administration could easily turn sour - or worse.
Her relations with the Europeans have already shown some signs of fraying since the British followed up their sinking of the Argentine cruiser General Belgrano with all-out military action to recapture the Falklands. This, despite French President Mitterrand's renewed declaration of support for Britain May 23 from the faraway Ivory Coast, where he is on an official visit.
Ireland and Italy have withdrawn from the originally solid European Community (EC) support for sanctions against Argentina. Renewal of the sanctions, due to expire May 24, came when EC foreign ministers met in Brussels that day. The ministers simultaneously urged Britain to keep the door open for a negotiated settlement with Argentina.
EC countries such as West Germany and Italy have - like the US - interests of their own in Latin America, and they do not want these put in jeopardy by too close an identification with a British policy seen in the hemisphere as colonialist and anti-Latin. In the case of Argentina, Italy cannot overlook the fact that roughly half that country's population is of Italian origin.
What of Argentina itself in this difficult confrontation? And of the Soviet Union, which is apparently giving Argentina its qualified support?
At this stage, of the two principals whose personal future is at stake in this conflict, Argentine President Galtieri is in much more immediate trouble than Mrs. Thatcher.
Some might caution that an unforeseen turn of events, such as the loss of one of the two British aircraft carriers off the Falklands, could still put Mrs. Thatcher's future at risk. But outright defeat for General Galtieri's junta in the military struggle for the Falklands could precipitate a major political upheaval involving his ousting, regardless of who or what took his place - a more ruthlessly nationalistic military group, Peronist populists, or outright left-wingers.
Who outside Argentina would be both capable and willing to commit themselves to the material help needed to reverse the tide of battle and ensure for General Galtieri victory on the field of battle?
Most of the rest of Latin America feels the need of hemispheric solidarity enough to have already tendered moral support. (Some of that may have backfired with the Panamanian representative's crude sexist remarks about Mrs. Thatcher in the UN Security Council May 23.) But whether any Latin country can or will proffer anything effective beyond that is open to question.
This leaves the Soviet Union. The Soviet tilt is clearly toward Argentina, yet still limited. Moscow is a net gainer from the present situation but presumably would not risk confrontation with the US over an issue as remote from the Soviet sphere of interest as the Falklands.
Although the Russians are reportedly helping the Argentines with intelligence from Soviet satellites, reports from London suggest Moscow's commitment to Argentina is not deep enough to prevent it halting purchases of Argentine grain now that it has difficulty in getting credits from Buenos Aires for them.
General Galtieri, a hard-line right-wing anticommunist at home, ''has repeatedly stated that (he) will not accept assistance, so to speak, from the Soviet Union or its proxies'' - to quote Secretary of State Haig in his May 23 television appearance.
''I would hope this situation would prevail,'' Mr. Haig added. ''The danger of it turning the other way is an active danger and one which we are very worried about.''