The election of 30-year-old lawyer of the far left to head the sometimes rambunctious youth wing of the Social Democratic Party has heaped still another problem in front of West Germany's already troubled chancellor, Helmut Schmidt.

The surprise narrow victory last week of Klaus-Uwe Benneter to head the young Socialists is widely viewed here as a sign that the more extreme left wing of Schmidt's own party may now be on a collision course with the much more moderate party establishment.

The young Socialists have had firebrands at the top before, but in the past year or so, they have been relatively quiet. This quiet period was a key factor in Schmidt's being able to squeak by in federal elections last October in which the mood of the voters clearly had swung toward middle-of-the-road and conservative views.

The prospect of a newly active youth wing advocating extreme leftist policies could clearly be a sign of "hard times head," as a Social Democratic party leader Egon Bahr, put it recently.

The immediate source of concern is that Benneter and the 149 delegates to the young Socialist congress who elected him by a four-vote majority, have already said they are willing to join forces with a Communist "committee for peace, disarmamement and cooperation" in demonstrations set for Frankfurt in May.

Bahr, one of Schmidt's key advisers, has warned that such cooperation could be grounds for expelling members from the party.

Theoretically, there are some 320,000 members in the Socialist youth group, basically all party members under 35. Only a relatively small percentage are on the far left of the left-center party. Still, the young Socialists under their new leader are a potential landmine for Schmidt, who is on the conservative side of his party.

What is worse for the chancellor is that Benneter comes along after a number of setbacks for Schmidt, and as more and more political leaders are asking what has happened to Schmidt's once-powerful leadership.

Last week, the social Democrats suffered unprecendented setbacks by conservatives in municipal elections in the state of Hesse, including the loss of key cities such as Frankfurt, Wiebaden and Darmstadt. These have been social Democrat strongholds since World War II.

The area is even called "Red Hesse."

Demonstrations by well-organized groups opposing nuclear power have growing in number and violence.Although opinion polls show the majority of West Germans still favor nuclear power, there is a growing feeling that Schmidt has has let the initiative pass to the demonstrators.

The coalition government, which includes the small Free Democratic Party, has also been hit by bugging scandals in recent weeks and still has not recovered from the angry reaction when it tried to stop an increase to pensioners that it had promised during the campaign.

Another source of concern for Schmidt is that he still has not met the new U.S. President. Schmidt had a very close and mutually supportive relationship with former President Ford and made strong use of that in domestic politics here.