BONN, West Germany (AP) _ A bitter power struggle is occurring over the publishing empire built by the late Axel Springer, with his wife, two friends and a longtime media industry rival fighting for control of the company.

The highly successful Springer empire, which has annual sales of about $1.6 billion, publishes West Germany's largest daily newspaper, Bild, and dozens of other mass-circulation publications.

Leo Kirch, another wealthy media entrepreneur, pooled his Springer shares with those of brothers Franz and Frieder Burda, also publishers, last month to amass a stake larger than that of Springer's heirs.

West German news media have dubbed the resulting power struggle '''Dallas' on the Elbe,'' in reference to the popular American soap opera and to the location of Hamburg - where Springer has publishing plants - on the Elbe River. ''I think this (dispute) will simmer down, and the sooner the better,'' Ernst Cramer, advisor to the Springer family, told The Associated Press in a telephone interview from his West Berlin office.

Cramer played down the feud, saying: ''The interests of the major shareholders are all the same - for the company to remain successful. This matter is not insurmountable.''

But Springer's widow, 45-year-old Friede Springer, has said in West German interviews that the affair has angered her.

''I am infinitely disappointed with the Burdas,'' the March 28 issue of the newsmagazine Der Spiegel quoted her as saying. ''I never imagined they would pull this kind of thing.''

A spokeswoman for Kirch, Armgard von Burgsdorff, insisted Kirch is interested only in the Springer company's continued success.

''The purpose of the agreement (with the Burda brothers) is to establish a stable majority, and to provide the publishing house with a leading role in a changing media world,'' she told the AP in a telephone interview from Kirch's Munich office.

Powers within the company have squabbled since 73-year-old Axel Springer died on Sept. 22, 1985, leaving his wife and two sons as direct heirs.

Springer built a family-owned empire that in addition to the 5 million daily-circulation Bild includes the respected conservative daily, Die Welt.

The day he died, the company stated that a few weeks earlier Springer had ''converted the company into a joint stock company.. .to safeguard the future of his holdings.'' Among the stockholders were the Burda brothers and Kirch.

Under a complicated formula, Springer's heirs and executors received control of about 26 percent of the company's shares, the Burda brothers 25.9 percent and Kirch 10 percent. The rest went to the stock exchange.

Kirch says that in addition to his 10 percent share, he has obtained support from owners of another 16 percent of Springer stock.

Mrs. Burgsdorff said the Springer heirs had agreed verbally in 1986 that Kirch should have a stake of up to 26 percent, but the family later changed its mind. She said Kirch then began discussions with the Burdas.

The Axel Springer Verlag company is overseen by a supervisory board, whose members include the Burdas and Mrs. Springer but not Kirch.

Kirch is involved in film distribution and production and other media areas. The Burda family owns the West German ''Bunte'' magazine and other publications.

Despite gaining more support through the Burdas and other shareholders, Kirch has not yet been able to overcome Mrs. Springer's opposition to his obtaining a seat on the supervisory board.

Mrs. Burgsdorff said Axel Springer had included Kirch in the shareholding formula ''because he knew Leo Kirch would be a strong media personality in the future.''

Neither Mrs. Springer nor the Burda brothers could be reached for comment on Tuesday.

Cramer, the Springer family advisor, said: ''For the family, the legacy of Axel Springer is important.''

But he added, ''This (dispute) almost had to come. Before it was owned by a family, now we are a shareholders' company.''