Burdened by wartime and colonial legacies but highly aware of their vulnerability, America's European allies are carefully laying the groundwork for their role in President Carter's challenges to Moscow over the Persian Gulf.

Nowhere more than in Europe did the president's declaration that the United States will fight to protect its strategic interests ring louder.

The Persian Gulf and its oil wealth are Europe's lifeline, and just as the U.S. allies in the North Atlantic Treaty Organization have moved in recent months to shore up the alliance, so too can Washington expect a responsiveness among the Europeans as it moves in the weeks and months ahead to fill in the blanks in the Carter doctrine.

U.S. policymakers have learned, however, that Europeans cannot be expected to fall into line automatically at Washington's every beck and call.

It took arm-twisting to win the support of key members of the NATO alliance for the recent decision to upgrade the European-based missile force. And Europe has been less than fully supportive in U.S. boycott efforts over the hostage crisis in Iran and the Soviet invasion of Afghanistan.

Now, President Carter has raised the stakes, threatening military action if the "vital interests" of the West in the persian Gulf are placed in jeopardy.

A survey of Washington Post correspondents in major European capitals shows that many of the continent's old insecurities about being caught in a superpower squeeze are coming to the surface.

Big enough to field sophisticated military establishments and in two cases, their own nuclear forces, the Europeans clearly see limits to the steps they can take in meeting a threat even to something as vital as their Persian Gulf oil supplies.

Some of the European hestitation is a reflection of the burdens of modern European history, some is bitter memories of retreats from empires, and some is pragmatic caution about pushing too hard on small countries with recent and none to happy recollections of past entanglements with Europe.

The U.N. reaction to Moscow's invasion of Afghanistan showed that small countries do not like being pushed around by larger ones. That sentiment is no less true, the Europeans caution Washington, even when the smaller countries would like a degree of protection.

Underlying the European reaction to President Carter's Wednesday speech is clear recognition of the importance of the Persian Gulf and its black gold.

French officials say Carter's drawing of a line in the gulf echoed sentiments President Valery Giseard d'Estaing has stressed in private to his ministers.

These officials say recognized and they are sure the Soviets recognized that when the United States talks about defending its "vital interests" that it is using the basic code that is understood on both sides of the ideological divide as meaning "this far and no further."

Britain, which has its independent source of oil in the North Sea, has been more public in welcoming the "new interest the U.S. is taking in the [gulf] area," as a key official put it in Parliament, and has been more willing to say that it at least will "consider" military action.

It is in West Germany that the signals become more ambivalent. Freighted with its 20th century history and on the front line of the East-West divide, the West Germans show anxiety at the prospect of big power military involvement in the Middle East.

Importing all of its oil and with 44 percent of those imports coming from the Persian Gulf, West Germany might be expected to jump quickly to the idea of military moves to protect its lifeline.

Yet, West German officials are quick to point out that their constitution prohibits Bonn from using its forces outside West German soil, and they stress their concern that even threats of force could upset what they call promising Western diplomatic and economic gains in the region.

Underlying this sentiment is a more ambiguous theme -- one reflective of Germany's recent tortured past.

As one former West German official put it, no Bonn spokesman would openly admit that he even would like to see West Germany fight in the to see West Germany fight in the Middle East, because any military involvement by Germans and the neighborhood of Israel would raise too many bad memories.

"You cannot quantify the problem but it is there," this knowledgeable West German said.

Such memories of the past weigh heavily on other Europeans as well.

Britain has by far the most experience in the region because of its colonial past. While it is showing a willingness to draw upon that experience, it is also a limiting factor.

In moves related to Iran as well as Afghanistan, Britian has quietly sent a small naval task force to join the American fleet in the Mediterranean. London also has sent Vice Adjutant General of the Army Michael Tomlinson to Kuwait, Bahrain, Qatar and Saudi Arabia to test the willingness of these states -- along with Oman -- to receive increased military aid and training from Britain.

Yet, the fiasco of the British-French-Israeli intervention over the Suez Canal in 1956 has left psychlogical scars on the British, scars that are a brutal reminder that the British lion's roar is barely a whisper east of Suez these days. A spate of recent books and television dramas recounting the Suez misadventure has served only to reopen old wounds.

These memories, and the presistent warnings from the Gulf states not to press for permanent bases, lead the British to caution against trying to get too much too fast.

While cooperating with the United States in building up the Indian Ocean island of Diego Garcia as a major base, Foreign Minister Lord Carrington said in Parliament last week that he did not "see at the moment any need to reestablish any substantial permanent U.K. military presence in the [gulf] area."

When all the plans are fleshed out in the coming months, officials in London say the overall offect will be increased training and supplies to the gulf and perhaps a greater naval presence, but no further military forces on the ground.

It is the British who have been the most outspoken in support of the United States about Iran and Afghanistan, but it is France that is in the position to make the most credible threats militarily in the Persian Gulf.

It is France that has developed a partroop and rapid intervention force -- a force it has used in Africa recently to protect French interests there and one tht French officials stress is capable of being used in other areas where French interests are at stake.

France gets more than two-thirds of its oil from the Persian Gulf.

This undoubtedly accounts for the decline in talk of a French evacuation of forces from its former colony of Djibouti. Strategically located on the African continent across from the southwest tip of the Arabian Peninsula, Djibouti is vital to any military operations in the region. A large portion of the French fleet is permanently on station in the Indian Ocean, and Djibouti is its main staging point. One of France's two aircraft carriers is usually in the region.

Thus, where Britain has virtually eliminated its presence east of Suez, France is very much a factor.

Despite the common interests, Paris shows no willingness, nor apparently is it any longer pushed, to resume an active role in NATO's military structure.

It is a question that does not really arise regarding the gulf, however as officials on both sides of the Atlantic stress that an steps that emerge in coming weeks, while including NATO in some areas, will be a matter of arrangements among individual nations that see a vital interest at stake. There are no suggestions that NATO's writ be extended to the gulf. West German Chancellor Helmut Schmidt rejected one such suggestion as "impudent talk" that would only serve to arouse mistrust" in the Middle East. "

Regardless of the specific steps that evolve in the coming months to underscore the Carter doctrine in the Persian Gulf, NATO countries already have made basic long-term decisions that will affect their military postures for years to come.

West Germany and Britain both have committed themselves to increase defense spending by an amount that is more than 3 percent above the amount necessary to keep pace with inflation. Britain, in addition, has revealed its multi-year, $10 billion program to update its aging independent nuclear deterrent of Polaris submarines and then to add to its fleet.

The increases in defense spending, along with the recent decision to introduce a new generation of missiles in Europe, have done much to reinvigorate the alliance, and the Soviet actions in Afghanistan appear to have removed the final barriers to recognition of interests beyond NATO boundaries.