The Western European allies are awakening to some troubling dilemmas posed by President Reagan's Strategic Defense Initiative that threaten to turn the research project into a political crisis for the Atlantic alliance.

Officials in several European capitals and at the North Atlantic Treaty Organization headquarters here are increasingly worried by SDI's potential for transatlantic conflict over the sharing of technology, the fate of arms control talks and the cohesion of western strategy.

British Adm. James Eberle, a former NATO commander who is now director of the Royal Institute of International Affairs in London, believes that the SDI project is "potentially the most divisive issue the alliance has faced."

Regardless of the military or technological feats that may emerge from the costly research program, Eberle says there is "considerable doubt as to whether any of the possible outcomes could be stabilizing."

Despite such apprehensions, Britain and West Germany appear inclined to participate because of the enormous economic and technological stakes involved. Italy and the Netherlands have adopted more reserved positions, but their governments are under strong pressure from industry to join the five-year, $26 billion program.

French President Francois Mitterrand has criticized the SDI project as "overarmament" and tried to persuade his partners to undertake a European space research program of their own. But that initiative has stalled and France is now promoting, along with Italy and West Germany, a combined European approach to SDI to maximize leverage with the United States.

Apart from their interest in staying abreast with U.S. research, the allies seem anxious to counter perceptions in Washington that they are shirking their own defense and succumbing to pacifist yearnings. "Europe is trying very hard on SDI not to be the eternal wimp," Britain's Eberle said.

At the same time, Western European countries want to avoid igniting another political row at home over NATO defense policy following the controversial deployment of Pershing II and cruise missiles that prompted Moscow to break off earlier arms control talks 16 months ago.

After earlier dismissals of the "Star Wars" plan, as it is popularly known, as too futuristic to affect them now, the allies were jolted last week by U.S. Defense Secretary Caspar W. Weinberger's invitation to declare within 60 days if they intended to participate in the project.

French presidential spokesman Michel Vauzelles mocked the offer as "a vague advertising circular" and West German officials rejected the deadline as "blackmail." In any case, the U.S. proposal, presented to a meeting of alliance defense ministers in Luxembourg, shook discussion of Europe's role in SDI from the realm of abstract theory to that of imminent decisions.

Although the NATO defense ministers signed a declaration of support last week for the U.S. research program, there is widespread anxiety across Europe that any economic or technological gains from the program will be overwhelmed by long-term political and strategic complications.

"It's really a no-win situation," a senior European official at NATO explained. "If we stay out, we will be accused of disloyalty to the Americans and missing out on a major leap ahead in high technology.

"But if we join, it raises some difficult questions: Do we really expect the Americans to share everything with us? Do we tell the peace movement types they were right all along, that nuclear deterrence is immoral and must be changed? Will the Russians react by agreeing to cut their missile force, or building new weapons to beat SDI?"

The spreading alliance debate over research into space-based defenses also reflects differing perceptions of how to deal with the Soviet Union.

Europeans have consistently urged detente and dialogue with Moscow as a way to promote mutual understanding of security interests in East and West.

But the $26 billion to be invested over the next five years in Star Wars research is considered by some Europeans to be another example of trying to extract Soviet cooperation through a "spend-them-into-the-ground" strategy that has failed in the past.

"The Russians have a capacity to suffer, perhaps greater than ours," said a West German specialist in East-West affairs. "Whatever they need to do to maintain parity, either through an offensive or defensive arms buildup, they will squeeze out of their people."

For the European allies, one of the most important issues is how SDI will affect the Geneva negotiations covering space, strategic and intermediate-range nuclear arms.

The Star Wars project is believed by many alliance officials to be a key reason why Moscow decided to return to the bargaining table. This rationale also holds that the Soviet Union will try to conclude a package deal rather quickly, involving missile cuts and a ban on space weapons, before SDI research pushes the West farther ahead in new technologies.

One concern among European allies is that at some point in the talks, the Soviets will propose to reduce both long-range and intermediate-range nuclear missiles in exchange for severe constraints on the SDI program.

If the Europeans find such an offer appealing but the Americans turn it down, a NATO official said, "that's when all hell will break loose in the alliance over SDI. It will make the quarreling over deployment of Pershing II and cruise missiles look like a love feast."

To some extent, divisions between the State Department and the Pentagon over the impact of SDI have been duplicated in internal struggles between European foreign and defense ministries.

At the Luxembourg meeting, European defense ministers displayed support for a project they generally view as a possible technology bonanza and a powerful bargaining chip in persuading Moscow to cut its missile force in exchange for any limits on space arms.

Foreign ministries in Bonn and London, however, have expressed skepticism about what one West German official called the "defense boys' traditional love for bigger budgets and more hi-tech toys."

In recent speeches, British Foreign Secretary Geoffrey Howe and his West German counterpart, Hans-Dietrich Genscher, have warned in muted fashion about the risks that SDI could erode the West's nuclear deterrence strategy.

By alluding to the possible creation of another "Maginot line," Howe pointed to the dangers that SDI might touch off an uncontrolled spiral of offensive weapons to overcome any new defensive shield.

Genscher noted that if nuclear weapons were neutralized, the Soviet Union would still be left with a superior arsenal of conventional weapons in Central Europe, a situation that might increase the chances of war.

Foreign Ministry officials in both capitals also expressed dismay about the enormous expense of developing an effective nuclear shield for the entire alliance. Such high costs could bankrupt efforts to maintain a conventional balance in Europe, the diplomats say.

In addition, Britain and France are worried that a leap ahead in antimissile systems or more effective offensive weapons to counter them could render obsolete their national nuclear deterrent forces that are poised to undergo expensive modernization.

So far, Western European leaders have adopted a cautiously loyal approach to the U.S. project, endorsing the idea of space research but stipulating that all work must remain within bounds of arms control treaties and that negotiations must precede any deployment.

Allied leaders generally agree that space research is justified to counter Soviet efforts in antimissile defense over the past decade. The Soviets have modernized the anti-missile defense system around Moscow that is allowed them under the 1972 Anti-Ballistic Missile Treaty. They have also engaged in laser experiments and recently "illuminated" one of their space satellites, presumably to test the strength of such rays, NATO officials said.

British Prime Minister Margaret Thatcher and West German Chancellor Helmut Kohl have already indicated a desire to see their countries' firms participate in the space research project. But both leaders insist there must be a full sharing of the economic benefits and technological know-how that emerge from the program.

"I responded to the U.S. initiative and said yes, of course, we will do research," Thatcher told reporters at the summit last weekend of European Community leaders. "It is exciting . . . We want our scientists to be involved."

Kohl, whose government has put off a final decision on joining in Star Wars research until later this year, indicated he was leaning toward approval when he admitted last weekend that "nonparticipation would result in a technological second-class status" for West Germany.

But Kohl's primary goal is to see drastic missile cuts by both superpowers, and he has suggested that he would gladly trade away the SDI program for such an accord. In a speech last month, Kohl said that deep cuts in missile forces on both sides could make deployment of space-based systems "increasingly superfluous."

Horst Teltschik, Kohl's chief foreign and security policy adviser, said the chancellor believes it is important for Europe to become involved in the SDI project so that it can influence future decisions about deployment and certify that European defense interests are being taken into account. Rejecting any role, Teltschik said, would nullify Europe's voice in a program the United States was determined to carry out anyway.

The seven-nation Western European Union hopes to thrash out a common approach to SDI at a meeting in Bonn April 22 and 23. The group is made up of France, Britain, Italy, West Germany, Belgium, the Netherlands and Luxembourg. The members believe a united front is the best way to guarantee equal access to economic and technological benefits with the United States.

But if a joint position cannot be worked out, Britain and West Germany have given notice that they will make individual arrangements with the United States to join the SDI research program.

The Bonn government has been enticed by U.S. claims that 90 percent of the work planned in the SDI project will have civilian spin-offs. More than 30 West German firms have been singled out by the Defense Ministry as possible participants in the program.

Two optical companies, Zeiss and Leitz, are said to be world leaders in the field of optic sensors, while the aeronautics firm MBB is one of the top manufacturers of space subsystems.

West German firms are also deemed highly advanced in such sectors as high-frequency signal processing, mirrors and reflectors, ultralight materials and components for hyperspeed rockets.