West Germany's new young defense minister -- whose style seems more American than German -- is causing a stir and some concern at NATO headquarters in Brussels, in some quarters of the Carter administration and even here in Germany.

"What Hans Apel is all about is what everybody wants to know," says one top U.S. diplomat in Europe, referring to the controversial 46-year-old German defense chief. Ten months after taking over as the civillan head of the largest and most important military partner of the United States in Western Europe, Apel remains a puzzle to many associates.

He has politely yet clearly challenged NATO's top military leader, Gen. Alexander Haig, on some key issues. He has not so politely broken the formality and club-like rules of NATO's inner circles by suggestions of weak leadership. And he has raised some provocative long-range questions about central issues affecting West German political as well as military security.

What is becoming clear, however, is that Apel -- a confidant and protege of Chancellor Helmut Schmidt -- is apt to be the most important West German defense minister of the postwar era.

That is so not simply because of the key role of any German defense chief, but also because Schmidt's role as the dominant and most popular political leader in West Germany continues to grow.

If Schmidt, 59, seeks and wins reelection in 1980, then Apel, in the view of many politicians, becomes probably the most likely Social Democrat to eventually succeed him.

"If you conclude we're going to have Schmidt around for another six years and Apel after him, then it pays for us to figure Apel out quickly," says one Western official.

"What is clear," another adds, "is that he is the new generation German. No ties to World War II. Never wore a uniform. No Nazi-era hang-ups. So he is taking a different tack. He is basically acting like an American politician who doesn't care if he breaks the china or where it breaks.

"We've reformed them," the official says of the postwar German generation. "And now we are finding it a little difficult to deal with them."

At NATO headquarters in Brussels, a Western diplomat says, "The Americans, especially, had gotten comfortably used to a certain kind of German defense minister who just took out his checkbook and said okay to the program."

Apel is different, he adds, "but some of the American attitudes persist, especially among the military people."

Like Schmidt, Apel comes from the bustling and tough northern city of Hamburg and he displays some of the brashness, wit and intellect of that city. Like Schmidt, who was a finance minister and defense minister before becoming chancellor, Apel was also a finance minister, which has made him somewhat more cost-conscious than some of his predecessors.

Also like Schmidt, Apel comes from a Social Democratic Party that has an outnumbered, yet active and out-spoken left wing. If he aspires to higher office he has got to consider party support across the board at some point.

Unlike Schmidt, however, Apel is young, closer to a new generation that has more doubts than their parents about Germany's becoming an increasingly larger military staging base for the Western alliance.

Apel is generally viewed as a middle-of-the-roader with a strong commitment to the need for the Western military alliance and West Germany's strong contribution to it. Nevertheless, he is the first defense chief never to have served in the military and to have made known his discomfort with uniforms in a book published three years ago, when he said he never wanted the defense job.

This week, West Germany's top military officer, Gen. Harald Wust, resigned, claiming he could not get along with Apel. Although Wust had run into criticism from some other quarters and was not viewed as a very dynamic leader, his departure also has raised questions about whether Apel will be able to establish a close relationship to Germany's armed forces.

Aside from the Wust episode, however, many observers and officials view Apel's political challenges as healthy and refreshing.

He has, for example, sought to remind NATO that it is the civilian political leaders and not the military leaders who have the final say on alliance questions.

He has sought to tone down the rhetoric and frequency of NATO military warnings to the public because he feels they can eventually overwhelm political considerations, which also must be taken into account, yet which may not have fully crystalized. Within this view, another concern is implicit: Political leaders have not spoken out sufficiently on some of these crucial East-West issues.

For example, Apel is known to be concerned that military arguments that the West needs new intermediate-range weapons to match a Soviet buildup can dim prospects of arm control negotiations handling such questions.

He is concerned that a new buildup of such weapons in Western Europe to match the Soviets could eventually "decouple" the U.S. commitment to defend Europe with long-range strategic weapons if necessary, or could add still more weapons to German soil, which may be politically unpopular to a new generation of voters.

At the heart of Apel and Schmidt's concern, informed sources say, is a feeling that the public, through military assessments, is becoming inundated with warnings about Soviet arms and the need to strengthen NATO while not paying enough attention to arms controls.

Schmidt, in particular, is known to feel that what he sees as an important formula, discussed here last May with Soviet President Leonid Brezhnev, is being overlooked. At that time, Brezhnev said neither side should seek military superiority and that approximate parity should be the goal.

Schmidt, perhaps for his own political benefit or for broader concerns, has sought repeatedly to draw attention to Brezhnev's visit here, though other Western officials tend not to see much new in it.

The German attitude on policy toward the Soviet Union creates much of the mystique of Schmidt and Apel these days.While both remain firmly committed to the West, Bonn clearly is trying to improve relations with the Soviets. This, however, is feeding ammunition to some conservative critics here and in the United States who feel Bonn's ties are somehow weakening, although there is no real evidence to support this.

Apel also has openly challenged Haig's philosophy of bigger NATO maneuvers each year in Germany. The maneuvers damage the countryside too much, he says, and perhaps send the wrong signals to the East.

At a NATO nuclear planning group meeting in Brussels last month, Apel, perhaps inadvertently, also vexed NATO Secretary General Joseph Luns by some undiplomatic language suggesting weak leadership. That eventually brought Luns to Bonn for a discussion with Schmidt.

Many of these challenges, however, have a certain aura of brashness or even frivolity, which has added to the enigma of Apel and raised questions about how serious he feels about certain issues.

He has repeatedly, for example, denied he has had squabbles with Haig and laughed off publicly any allusion to troubles with Luns or NATO when numerous officials close to the situation confirm the concern in those quarters.

The Germans like Haig as a military commander but want to reinforce the supremacy of civilian leadership and increasingly are wary of his possible political ambitions, especially if he uses Germany to become "Mister NATO," as one critic calls him.

On balance, one senior NATO official says that despite Apel's controversial start, the alliance is "not uncomfortable with him," values his political future and his clout in Bonn and views him as reflective of Germany's growing self-assertiveness.

An experienced U.S. official describes White House and NATO views of Apel as "a lot of curious excitement."

Though nobody outside Apel's tight German circle boasts of knowing him well, one U.S. diplomat says, "I don't regard him as a finished character yet. You can't put him in a convenient pigeonhole. I think he is still trying to find himself in this enormously important post. But we've got to work hard on the Germans, too."